LCM & HCF Word Problems: Mixed Questions with Answers
- Vaishnavi has 24 red beads and 36 blue beads. She wants to make the greatest possible number of identical groups using all the beads. How many groups can she make?
Answer: 12 groups - Two bells ring at intervals of 12 minutes and 18 minutes. If they ring together at 9:00 a.m., after how many minutes will they ring together again?
Answer: 36 minutes - Find the greatest number that divides 48 and 72 exactly.
Answer: 24 - Find the least number that is exactly divisible by 15, 20 and 30.
Answer: 60 - A shop has 45 apples and 60 oranges. The fruits are to be packed into identical baskets with no fruit left over. What is the greatest number of baskets possible?
Answer: 15 baskets - Two lights flash every 8 seconds and 12 seconds. If they flash together now, after how many seconds will they flash together again?
Answer: 24 seconds - Find the HCF of 84 and 126.
Answer: 42 - Find the LCM of 16 and 24.
Answer: 48 - Three buses leave a station every 15, 20 and 30 minutes. If they leave together at 8:00 a.m., when will they next leave together?
Answer: 9:00 a.m. - A teacher has 72 pencils and 96 erasers. She wants to distribute them into the greatest possible number of identical sets. How many sets can she make?
Answer: 24 sets - Find the greatest number that divides 96, 144 and 192 exactly.
Answer: 48 - Find the smallest number that is divisible by 18, 24 and 36.
Answer: 72 - Two runners complete a lap in 20 seconds and 30 seconds respectively. If they start together, after how many seconds will they both be at the starting point together again?
Answer: 60 seconds - A florist has 54 roses and 81 lilies. She wants to make identical bouquets using all the flowers. What is the greatest number of bouquets she can make?
Answer: 27 bouquets - Find the HCF of 108 and 180.
Answer: 36 - Find the LCM of 25 and 40.
Answer: 200 - Three machines beep every 6, 8 and 12 minutes. If they beep together at 10:00 a.m., when will they beep together again?
Answer: 10:24 a.m. - A school has 84 boys and 126 girls. They are to be divided into the greatest possible number of equal groups, with the same number of boys and girls in each group. How many groups can be made?
Answer: 42 groups - Find the greatest number that divides 120 and 168 exactly.
Answer: 24 - Find the smallest number divisible by 12, 15 and 20.
Answer: 60 - Two alarms ring every 14 minutes and 21 minutes. If they ring together at 7:30 a.m., when will they ring together again?
Answer: 8:12 a.m. - A shopkeeper has 64 chocolates and 80 candies. He wants to make identical packets with no item left. What is the greatest number of packets he can make?
Answer: 16 packets - Find the HCF of 144 and 216.
Answer: 72 - Find the LCM of 18 and 27.
Answer: 54 - A bus arrives every 24 minutes and a train arrives every 36 minutes. If both arrive together at 6:00 a.m., when will they next arrive together?
Answer: 7:12 a.m. - There are 90 mangoes and 120 bananas. They are to be divided into identical groups with no fruit left. What is the greatest number of groups?
Answer: 30 groups - Find the greatest number that divides 135 and 180 exactly.
Answer: 45 - Find the least number divisible by 16, 20 and 24.
Answer: 240 - Two bells ring every 18 minutes and 24 minutes. If they ring together at 11:00 a.m., when will they ring together again?
Answer: 12:12 p.m. - A teacher has 108 notebooks and 144 pencils. She wants to distribute them into the greatest possible number of identical sets. How many sets can she make?
Answer: 36 sets - Find the HCF of 156 and 234.
Answer: 78 - Find the LCM of 28 and 42.
Answer: 84 - Three traffic lights change every 20, 30 and 40 seconds. If they change together now, after how many seconds will they change together again?
Answer: 120 seconds - A farmer has 75 kg of rice and 125 kg of wheat. He wants to pack them into identical bags with no material left. What is the greatest number of bags possible?
Answer: 25 bags - Find the greatest number that divides 180, 240 and 300 exactly.
Answer: 60 - Find the smallest number divisible by 21, 28 and 42.
Answer: 84 - Two cyclists complete a round in 24 minutes and 32 minutes. If they start together, after how many minutes will they meet at the starting point again?
Answer: 96 minutes - A school has 96 red flags and 144 blue flags. They are to be arranged into identical groups. What is the greatest number of groups possible?
Answer: 48 groups - Find the HCF of 198 and 264.
Answer: 66 - Find the LCM of 32 and 48.
Answer: 96 - Three sprinklers work every 12, 18 and 24 minutes. If they start together at 6:00 a.m., when will they start together again?
Answer: 7:12 a.m. - A fruit seller has 120 apples and 180 oranges. He wants to make identical baskets using all the fruits. What is the greatest number of baskets?
Answer: 60 baskets - Find the greatest number that divides 210 and 294 exactly.
Answer: 42 - Find the smallest number divisible by 24, 36 and 54.
Answer: 216 - Two bells ring every 16 minutes and 24 minutes. If they ring together at 2:00 p.m., when will they ring together again?
Answer: 2:48 p.m. - A class has 72 boys and 120 girls. They are divided into the greatest possible number of equal groups. How many groups can be made?
Answer: 24 groups - Find the HCF of 225 and 315.
Answer: 45 - Find the LCM of 36 and 48.
Answer: 144 - A machine completes a cycle every 15 seconds and another every 25 seconds. If both start together, after how many seconds will they start together again?
Answer: 75 seconds - A shopkeeper has 128 pens and 160 pencils. He wants to make identical stationery sets using all the items. What is the greatest number of sets?
Answer: 32 sets - The HCF of two numbers is 12 and their LCM is 180. If one number is 36, find the other number.
Answer: 60 - The HCF of two numbers is 15 and their LCM is 300. If one number is 60, find the other number.
Answer: 75 - Two numbers are 48 and 72. Find their HCF and LCM.
Answer: HCF = 24, LCM = 144 - Two numbers are 60 and 90. Find their HCF and LCM.
Answer: HCF = 30, LCM = 180 - The product of two numbers is 2,160. Their HCF is 12 and one number is 36. Find the other number and LCM.
Answer: 60 and 180 - The product of two numbers is 5,760. Their HCF is 24 and one number is 96. Find the other number and LCM.
Answer: 60 and 240 - Two numbers have an HCF of 18 and an LCM of 540. If one number is 90, find the other number.
Answer: 108 - Two numbers have an HCF of 20 and an LCM of 600. If one number is 120, find the other number.
Answer: 100 - Two numbers are 84 and 126. Find their HCF and LCM.
Answer: HCF = 42, LCM = 252 - Two numbers are 96 and 144. Find their HCF and LCM.
Answer: HCF = 48, LCM = 288 - A number is divisible by 12, 18 and 24. What is the smallest possible number?
Answer: 72 - Find the greatest number that divides 252, 336 and 420 exactly.
Answer: 84 - Three bells ring every 10, 15 and 25 minutes. If they ring together at 9:00 a.m., when will they ring together again?
Answer: 11:30 a.m. - A bakery has 144 buns and 192 cakes. They are to be packed into the greatest possible number of identical boxes. How many boxes can be made?
Answer: 48 boxes - Find the LCM of 45 and 60.
Answer: 180 - Find the HCF of 240 and 360.
Answer: 120 - Two lights blink every 18 seconds and 30 seconds. If they blink together now, after how many seconds will they blink together again?
Answer: 90 seconds - A gardener has 168 red flowers and 252 white flowers. He wants to make identical bouquets using all the flowers. What is the greatest number of bouquets?
Answer: 84 bouquets - Find the smallest number that leaves no remainder when divided by 15, 25 and 30.
Answer: 150 - Find the greatest number that divides 270, 360 and 450 exactly.
Answer: 90 - Two buses arrive every 18 minutes and 27 minutes. If they arrive together at 8:00 a.m., when will they next arrive together?
Answer: 9:06 a.m. - A teacher has 150 blue pens and 210 black pens. She wants to make identical packs using all the pens. What is the greatest number of packs?
Answer: 30 packs - Two numbers have an HCF of 24 and an LCM of 720. If one number is 144, find the other number.
Answer: 120 - The product of two numbers is 18,900. Their HCF is 45 and one number is 135. Find the other number and LCM.
Answer: 140 and 420 - Two numbers are 120 and 180. Find their HCF and LCM.
Answer: HCF = 60, LCM = 360 - Two numbers are 144 and 240. Find their HCF and LCM.
Answer: HCF = 48, LCM = 720 - A school bell rings every 20 minutes and another bell rings every 30 minutes. If both ring at 10:00 a.m., when will they ring together again?
Answer: 11:00 a.m. - There are 180 apples and 240 oranges. They are to be distributed equally into the greatest possible number of baskets. How many baskets can be made?
Answer: 60 baskets - Find the smallest number divisible by 18, 30 and 45.
Answer: 90 - Find the greatest number that divides 320, 400 and 480 exactly.
Answer: 80 - Two machines complete a cycle every 24 seconds and 40 seconds. If they start together, after how many seconds will they start together again?
Answer: 120 seconds - A shopkeeper has 216 notebooks and 288 pencils. He wants to make identical sets using all the items. What is the greatest number of sets?
Answer: 72 sets - The HCF of two numbers is 16 and their LCM is 480. If one number is 96, find the other number.
Answer: 80 - The product of two numbers is 28,800. Their HCF is 48 and one number is 144. Find the other number and LCM.
Answer: 200 and 600 - Two numbers are 168 and 252. Find their HCF and LCM.
Answer: HCF = 84, LCM = 504 - Two numbers are 180 and 300. Find their HCF and LCM.
Answer: HCF = 60, LCM = 900 - Three buses leave every 12, 16 and 24 minutes. If they leave together at 7:00 a.m., when will they next leave together?
Answer: 8:12 a.m. - A farmer has 240 kg of rice and 360 kg of wheat. He wants to pack them into the greatest possible number of identical bags. How many bags can he make?
Answer: 120 bags - Find the smallest number divisible by 20, 30, 40 and 60.
Answer: 120 - Find the greatest number that divides 360, 480 and 600 exactly.
Answer: 120 - Two lights flash every 15 seconds and 20 seconds. If they flash together now, after how many seconds will they flash together again?
Answer: 60 seconds - A school has 240 boys and 360 girls. They are to be divided into the greatest possible number of identical groups. How many groups can be formed?
Answer: 120 groups - The HCF of two numbers is 25 and their LCM is 750. If one number is 125, find the other number.
Answer: 150 - The product of two numbers is 40,320. Their HCF is 56 and one number is 224. Find the other number and LCM.
Answer: 180 and 720 - Two numbers are 225 and 375. Find their HCF and LCM.
Answer: HCF = 75, LCM = 1,125 - Two numbers are 288 and 432. Find their HCF and LCM.
Answer: HCF = 144, LCM = 864 - Four bells ring at intervals of 6, 8, 12 and 24 minutes. If they ring together at 8:00 a.m., when will they ring together again?
Answer: 8:24 a.m. - A fruit seller has 300 apples and 450 oranges. He wants to make identical baskets using all the fruits. What is the greatest number of baskets he can make?
Answer: 150 baskets - Find the smallest number that is exactly divisible by 24, 30, 40 and 60.
Answer: 120 - The product of two numbers is 54,000. Their HCF is 90 and one number is 300. Find the other number and LCM.
Answer: 180 and 600