Question

What is the least common multiple of 40, 13, and 10?​

Answer 1

520

Explanation:

The least common multiple of 13, 10 and 40 is the smallest positive integer that divides the numbers 13, 10 and 40 without a remainder.

That would 520 because it could be divided into 13, 10 and 40 without a remainder.

520 divided by 10= 52

520 divided by 13= 40

520 divided by 40= 13

Answer 2

List all prime factors for each number.

Prime Factorization of 10 is:
2 x 5 => 21 x 51

Prime Factorization of 13 shows:
13 is prime => 131

Prime Factorization of 40 is:
2 x 2 x 2 x 5 => 23 x 51

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is
2, 2, 2, 5, 13

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 5 x 13 = 520

In exponential form:
LCM = 23 x 51 x 131 = 520

LCM = 520

Therefore,

LCM(10, 13, 40) = 520