How can you find the common multiples and least common multiples of two numbers?

Answer 1

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the highest amount of each factor.

2 x 3 x 5 x 7 = 210, the LCM

Multiples of 210 will all be common multiples of 30 and 42 and can be found by multiplying 210 by successive counting numbers.

210 x 1 = 210

210 x 2 = 420

210 x 3 = 630 and so on.

Answer 2

The quickest way to find a common multiple of two numbers is to multiply the two numbers together. Keep adding that number to itself and the results will all be common multiples. The LCM usually requires some factoring. Example: 30 and 42

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Combine the factors, eliminating duplicates.

2 x 3 x 5 x 7 = 210, the LCM