How do you find the least common multiple of three numbers?

Answer 1

The LCM can be found by taking the multiple of the highest power of prime factors from all numbers. For example, the LCM of 28, 98, and 350 is 4900, which is the multiple of the highest power of prime factors from all three numbers.

28 = 2^2 x 7

98 = 2 x 7^2

350 = 2 x 5^2 x 7

and 2^2 x 5^2 x 7^2 = 4 x 25 x 49 = 4900.

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Another example : the LCM of 28, 39, and 42

28 = 2^2 x 7

39 = 3 x 13

42 = 2 x 3 x 7

Except for 2, the factors all have the exponent (1), i.e. 3 = 3^1

and 2^2 x 3^1 x 7^1 x 13^1 = 4 x 3 x 7 x 13, for an LCM of 1092

You can find that

1092 = 28 x 39

1092 = 39 x 28

1092 = 42 x 26

and there is no smaller number that is a multiple of all three.

Answer 2

If you use the method that involves finding the prime factors, the method is basically the same, whether you find the least common multiple of two numbers, of three numbers, of four numbers, etc.