What is the least common multiple of 50 and 60?

Answer 1

The LCM of 50 and 60 is 300, which is the multiple of the highest power of prime factors from both numbers (22 x 3 x 52 = 2 x 2 x 3 x 5 x 5 = 300).

Alternate Method:

The least common multiple of two numbers is their product divided by their greatest common factor. Therefore, the least common multiple of 50 and 60 is the product of 50 and 60 divided by their greatest common factor.

The greatest common factor of 50 and 60 is 10. (For information on this, see the Related Question "What is the greatest common factor of 50 and 60".)

So, the LCM is 50 x 60 ÷ 10 = 300
To determine the LCM, you must first write out (or imagine in your head) all the multiples of each number. The multiples of 50 are 50, 100, 150, 200, 250, 300, 350, 400, 450, etc. The multiples of 60 are 60, 120, 180, 240, 300, 360, 420, 480, etc. Now, search the list for the smallest number that appears in both lists. That's the LCM. In this case, it's 300.

Answer 2

300