Find LCM and HCF (Word Problems)

1. Two bells ring at intervals of 6 minutes and 8 minutes. After how many minutes will they ring together?
2. A gardener has 45 roses and 60 lilies. He wants to make bouquets with equal flowers. What is the maximum number of bouquets he can make?
3. A bus arrives at a stop every 15 minutes, and another every 25 minutes. After how long will both arrive together?
4. Three rods are of lengths 42 cm, 56 cm, and 70 cm. Find the greatest length of rod that can measure all three exactly.
5. A traffic light blinks every 12 seconds and another every 18 seconds. When will they blink together again?
6. A fruit seller has 84 apples and 98 oranges. He wants to make baskets with equal fruits. What is the greatest number of baskets he can make?
7. Ravi takes 20 minutes to walk around a park and his friend takes 30 minutes. After how long will they meet at the starting point?
8. The greatest number which divides 105 and 165 exactly is?
9. Three bells ring at 9, 12, and 15 minutes intervals. After how long will they ring together?
10. A ribbon of 72 cm and another of 108 cm is to be cut into equal pieces. Find the maximum length of each piece.
11. A child jumps 12 times a minute and another jumps 15 times a minute. After how many jumps will both land together?
12. There are 96 pencils and 120 pens. Find the greatest number of sets that can be made without any remainder.
13. A clock strikes every 20 minutes, another strikes every 25 minutes. When will they strike together?
14. Find the greatest length that can measure exactly 36 m and 48 m.
15. One tap fills a tank in 12 minutes, another in 16 minutes. After how many minutes will both complete together?
16. Find the largest length of rope that can be cut from 90 m and 150 m without any remainder.
17. A farmer waters plants every 18 days, and another farmer waters every 24 days. After how many days will they water together?
18. A shopkeeper has 72 candies and 108 chocolates. He wants to make packets with equal numbers. What is the maximum number of packets?
19. A train crosses a station every 36 minutes and another every 54 minutes. After how long will both cross together?
20. Find the greatest number that divides 84, 126, and 210 exactly.
21. A boy takes 45 seconds to complete one round of the ground and another takes 75 seconds. After how long will they meet at the starting point?
22. The side of one square is 81 cm and another is 63 cm. Find the largest square tile that can cover both exactly.
23. Two buses start together, one runs every 42 minutes, and the other every 56 minutes. After how long will they meet again?
24. Find the HCF of 72, 96, and 120.
25. Two bulbs blink every 25 seconds and 40 seconds. After how many seconds will they blink together?
26. A teacher wants to distribute 144 books and 180 notebooks equally among students. What is the maximum number of students?
27. A boy jumps every 28 seconds and his friend jumps every 35 seconds. After how many seconds will they jump together?
28. Find the largest number that divides 126 and 198 exactly.
29. A festival is celebrated every 24 years, another every 36 years. After how many years will they be celebrated together?
30. Find the HCF of 150 and 225.
31. A bell rings every 8 minutes and another every 12 minutes. When will they ring together again?
32. Find the largest number that divides 132, 198, and 330 exactly.
33. A bus leaves every 45 minutes and another every 75 minutes. After how long will both leave together?
34. Find the HCF of 68 and 102.
35. Two runners take 60 seconds and 90 seconds to complete a round. After how long will they meet at the start?
36. A fruit seller has 144 oranges and 216 apples. He wants to pack them equally. What is the maximum number of packets?
37. A drum beats every 18 minutes and another every 24 minutes. When will they beat together again?
38. Find the largest square tile that can exactly cover a floor of dimensions 252 cm × 198 cm.
39. A lift stops every 20 floors and another every 30 floors. After how many floors will both stop together?
40. A teacher has 60 red pens and 84 blue pens. What is the greatest number of sets she can make?
41. A ferry arrives every 10 minutes and another every 15 minutes. After how many minutes will both arrive together?
42. Find the HCF of 120 and 160.
43. Two friends go jogging. One completes a round in 32 minutes and the other in 48 minutes. After how many minutes will they meet?
44. A farmer has 72 mangoes and 90 guavas. He wants to distribute equally. What is the maximum number of baskets?
45. A bulb glows every 9 minutes and another every 21 minutes. When will they glow together?
46. Find the largest number that divides 108 and 135 exactly.
47. Two machines release whistles every 18 minutes and 27 minutes. After how long will they whistle together?
48. A mason has 180 bricks and 240 stones. What is the greatest number of sets he can make?
49. A bell tolls every 40 minutes and another every 60 minutes. After how long will they toll together?
50. Find the largest length of stick that can measure 64 cm and 96 cm exactly.
51. A train blows a whistle every 72 minutes, another every 90 minutes. After how long will both blow together?
52. A shopkeeper has 135 pencils and 180 erasers. He wants to make equal packs. What is the greatest number of packs?
53. A boy jumps rope every 24 seconds, his friend every 36 seconds. After how long will they jump together?
54. Find the largest number that divides 210 and 315 exactly.
55. Two traffic signals change every 45 seconds and 60 seconds. After how many seconds will they change together?
56. A farmer has 256 apples and 320 oranges. He wants to put them in equal boxes. What is the greatest number of boxes?
57. Two ferries arrive every 18 minutes and 30 minutes. After how many minutes will they arrive together?
58. A tailor has 96 m of red cloth and 120 m of blue cloth. He wants to cut equal pieces. What is the maximum length of each piece?
59. A boy claps every 25 seconds and his friend every 35 seconds. After how many seconds will they clap together?
60. Find the HCF of 84 and 126.
61. A bell rings every 12 minutes and another every 20 minutes. After how long will they ring together?
62. Find the largest number that divides 270 and 360 exactly.
63. A bus starts every 48 minutes, another every 60 minutes. After how long will they meet again?
64. A school has 128 boys and 192 girls. What is the maximum number of groups they can be divided into equally?
65. A drummer beats his drum every 16 minutes, another every 24 minutes. After how long will they beat together?
66. Find the largest number that divides 72, 108, and 180 exactly.
67. A boy cycles a round in 18 minutes, another in 27 minutes. After how many minutes will they meet again?
68. Find the HCF of 256 and 384.
69. A traffic light changes every 50 seconds and another every 75 seconds. After how long will they change together?
70. A shopkeeper has 240 chocolates and 300 biscuits. What is the greatest number of packets he can make?
71. A bell rings every 7 minutes and another every 21 minutes. After how long will they ring together?
72. A gardener has 150 tulips and 225 roses. He wants to make bouquets equally. What is the maximum number of bouquets?
73. A child jumps 30 times a minute and another 45 times a minute. After how many jumps will they land together?
74. Find the largest number that divides 96 and 128 exactly.
75. Two buses leave a station every 35 minutes and 42 minutes. After how long will both leave together?
76. A tailor has 84 m of cloth and 126 m of cloth. What is the maximum length of each piece he can cut?
77. A boy claps every 40 seconds, another every 50 seconds. After how many seconds will they clap together?
78. Find the HCF of 144 and 216.
79. Two festivals occur every 36 years and 48 years. After how many years will they occur together?
80. A shopkeeper has 75 kg rice and 90 kg wheat. He wants to pack them equally. What is the maximum weight of each bag?
81. A bell tolls every 18 minutes, another every 30 minutes. After how long will they toll together?
82. Find the largest number that divides 252 and 378 exactly.
83. A boy completes a game round in 42 minutes, another in 63 minutes. After how many minutes will they meet at start?
84. A farmer has 180 bananas and 270 mangoes. He wants to distribute equally. What is the maximum number of baskets?
85. Two machines start every 28 minutes and 42 minutes. After how many minutes will they start together?
86. A teacher has 210 pens and 315 pencils. What is the greatest number of sets she can make?
87. A bulb glows every 15 minutes, another every 20 minutes. After how long will they glow together?
88. Find the largest number that divides 324 and 540 exactly.
89. A bell rings every 9 minutes and another every 18 minutes. After how long will they ring together?
90. A shopkeeper has 225 biscuits and 300 toffees. What is the greatest number of packets he can make?
91. A ferry arrives every 36 minutes, another every 48 minutes. After how many minutes will they arrive together?
92. Find the HCF of 132 and 198.
93. Two boys play drum beats every 60 seconds and 90 seconds. After how long will they beat together?
94. A school has 72 students in one class and 108 in another. What is the maximum number of groups possible?
95. A bus arrives every 42 minutes and another every 56 minutes. After how many minutes will they arrive together?
96. Find the largest number that divides 128 and 192 exactly.
97. Two lights blink every 35 minutes and 49 minutes. After how many minutes will they blink together?
98. A fruit seller has 154 mangoes and 231 bananas. What is the greatest number of baskets he can make?
99. A clock strikes every 18 minutes and another every 24 minutes. After how long will they strike together?
100. Find the HCF of 72 and 120.

Answers

1. 24
   
2. 15
   
3. 75
   
4. 14
   
5. 36
   
6. 14
   
7. 60
   
8. 15
   
9. 180
   
10. 36
    
11. 60
    
12. 24
    
13. 100
    
14. 12
    
15. 48
    
16. 30
    
17. 72
    
18. 36
    
19. 108
    
20. 42
    
21. 225
    
22. 9
    
23. 168
    
24. 24
    
25. 200
    
26. 36
    
27. 140
    
28. 18
    
29. 72
    
30. 75
    
31. 24
    
32. 66
    
33. 225
    
34. 34
    
35. 180
    
36. 72
    
37. 72
    
38. 18
    
39. 60
    
40. 12
    
41. 30
    
42. 40
    
43. 96
    
44. 18
    
45. 63
    
46. 27
    
47. 54
    
48. 60
    
49. 120
    
50. 32
    
51. 360
    
52. 45
    
53. 72
    
54. 105
    
55. 180
    
56. 64
    
57. 90
    
58. 24
    
59. 175
    
60. 42
    
61. 60
    
62. 90
    
63. 240
    
64. 64
    
65. 48
    
66. 36
    
67. 54
    
68. 128
    
69. 150
    
70. 60
    
71. 21
    
72. 75
    
73. 90
    
74. 32
    
75. 210
    
76. 42
    
77. 200
    
78. 72
    
79. 144
    
80. 15
    
81. 90
    
82. 126
    
83. 126
    
84. 90
    
85. 84
    
86. 105
    
87. 60
    
88. 108
    
89. 18
    
90. 75
    
91. 144
    
92. 66
    
93. 180
    
94. 36
    
95. 168
    
96. 64
    
97. 245
    
98. 77
    
99. 72
    
100. 24