What is the least common multiple of 90 and 60?

Answer 1

To determine the least common multiple of two numbers, determine the prime factors of both numbers. Then, determine the prime factors they have in common. Multiply all their prime factors together (in other words, multiply both numbers together) and divide by the prime factors they have in common (in other words, their greatest common factor).

The prime factors of 60 are 2, 2, 3, and 5.

The prime factors of 90 are 2, 3, 3, and 5.

The prime factors in common are 2, 3, and 5, so the greatest common factor is 2 x 3 x 5 = 30. The least common multiple is thus (2 x 2 x 3 x 5) x (2 x 3 x 3 x 5) ÷ (2 x 3 x 5) or 60 x 90 ÷ 30 = 180.

A similar way to use the prime factors is to take the prime factors of one number and cross out any that appear in the other number, then multiply the remaining ones together to calculate the least common multiple.

60 has 2, 2, 3, and 5

90 are 2, 3, 3, and 5

The least common multiple of 60 and 90 is 2 x 2 x 3 x 5 x 3 = 180.

Answer 2

The least common multiple of the numbers 90 and 60 is 180.