What is the greatest common multiple for the numbers 1-100?

Answer 1

101

Answer 2

There is no greatest common multiple: for whatever value you say is the greatest I can always add their lowest common multiple and get an even greater common multiple.

There is a greatest common FACTOR and a LOWEST common multiple:

gcf(1..100) = 1

lcm(1..100) = 69,720,375,229,712,477,164,533,808,935,312,303,556,800

Using the factorisation method:

2 = 2

3 = 3

4 = 2^2

5 = 5

6 = 2 x 3

7 = 7

8 = 2^3

9 = 3^2

10 = 2 x 5

11 = 11

12 = 2^2 x 3

13 = 13

14 = 2 x 7

15 = 3 x 5

16 = 2^4

17 = 17

18 = 2 x 3^2

19 = 19

20 = 2^2 x 5

21 = 3 x 7

22 = 2 x 11

23 = 23

24 = 2^3 x 3

25 = 5^2

26 = 2 x 13

27 = 3^3

28 = 2^2 x 7

29 = 29

30 = 2 x 3 x 5

31 = 31

32 = 2^5

33 = 3 x 11

34 = 2 x 17

35 = 5 x 7

36 = 2^2 x 3^2

37 = 37

38 = 2 x 19

39 = 3 x 13

40 = 2^3 x 5

41 = 41

42 = 2 x 3 x 7

43 = 43

44 = 2^2 x 11

45 = 3^2 x 5

46 = 2 x 23

47 = 47

48 = 2^4 x 3

49 = 7^2

50 = 2 x 5^2

51 = 3 x 17

52 = 2^2 x 13

53 = 53

54 = 2 x 3^3

55 = 5 x 11

56 = 2^3 x 7

57 = 3 x 19

58 = 2 x 29

59 = 59

60 = 2^2 x 3 x 5

61 = 61

62 = 2 x 31

63 = 3^2 x 7

64 = 2^6

65 = 5 x 13

66 = 2 x 3 x 11

67 = 67

68 = 2^2 x 17

69 = 3 x 23

70 = 2 x 5 x 7

71 = 71

72 = 2^3 x 3^2

73 = 73

74 = 2 x 37

75 = 3 x 5^2

76 = 2^2 x 19

77 = 7 x 11

78 = 2 x 3 x 13

79 = 79

80 = 2^4 x 5

81 = 3^4

82 = 2 x 41

83 = 83

84 = 2^2 x 3 x 7

85 = 5 x 17

86 = 2 x 43

87 = 3 x 29

88 = 2^3 x 11

89 = 89

90 = 2 x 3^2 x 5

91 = 7 x 13

92 = 2^2 x 23

93 = 3 x 31

94 = 2 x 47

95 = 5 x 19

96 = 2^5 x 3

97 = 97

98 = 2 x 7^2

99 = 3^2 x 11

100 = 2^2 x 5^2

hcf = 1

lcm = 2^6 x 3^4 x 5^2 x 7^2 x 11 x 13 x 17 x 19 x 23 x 29 x 31 x 37 x 41 x 43 x 47 x 53 x 59 x 61 x 67 x 71 x 73 x 79 x 83 x 89 x 97 = 69720375229712477164533808935312303556800