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Transcript 
A common multiple of two natural numbers is a number that is a multiple of
both numbers. For example, 42 is a common multiple of 6 and 14, because
42 = 6 • 7 and 42 = 14 • 3. The least common multiple (LCM) of two natural
numbers is the smallest number that is a multiple of both.
EXAMPLE
Find the least common multiple of 24 and 30.
First write the prime factorization of each number.
24 = 2 • 2 • 2 • 3
SOLUTION
30 = 2 • 3 • 5
䉴
The least common multiple is the product of the common prime factors and
all the prime factors that are not common. The least common multiple of 24
and 30 is 2 • 3 • 2 • 2 • 5 = 120.
PRACTICE
List all the factors of the number.
1. 18
2. 10
3. 77
4. 35
5. 27
6. 100
7. 42
8. 49
11. 121
12. 150
9. 52
10. 81
Write the prime factorization of the number if it is not a prime number. If a
number is prime, write prime.
13. 27
14. 24
15. 32
16. 61
17. 55
18. 68
19. 48
20. 225
21. 90
22. 75
23. 39
24. 1000
25. 728
26. 101
27. 512
28. 210
List all the common factors of the pair of numbers.
29. 15, 30
30. 36, 54
31. 5, 20
32. 14, 21
33. 9, 36
34. 24, 28
35. 20, 55
36. 12, 30
Find the greatest common factor of the pair of numbers.
37. 25, 30
38. 32, 40
39. 17, 24
40. 35, 150
41. 14, 28
42. 65, 39
43. 102, 51
44. 128, 104
45. 36, 50
46. 45, 135
47. 29, 87
48. 35, 48
49. 56, 70
50. 88, 231
51. 47, 48
52. 93, 124
Find the least common multiple of the pair of numbers.
53. 5, 7
54. 3, 4
55. 3, 16
56. 7, 12
57. 4, 12
58. 9, 15
59. 12, 35
60. 6, 14
61. 20, 25
62. 10, 24
63. 3, 17
64. 15, 40
65. 70, 14
66. 36, 50
67. 22, 30
778
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