Question

The least number divisible by each of the numbers $15,20,24,32and36$ is

Answer 1

The least number divisible by each of the numbers $15,20,24,32$ and $36$ is the LCM of these numbers.

Use prime factorization to find the LCM

First resolve the numbers into prime factors.

$15=3\times 5$

$20=2\times 2\times 5=2^2\times 5$

$24=2\times 2\times 2\times 3=2^3\times 3$

$32=2\times 2\times 2\times 2\times 2=2^5$

$36=2\times 2\times 3\times 3=2^2\times 3^2$

Now the least common factor (LCM) is equal to the product of all factors with the highest powers.

$LCM=2^5\times 3^2\times 5$

$=1440$