Question

What is the least number which when decreased by $5$ is divisible by $36,48,21$ and $28$?

Answer 1

To find the least number, we need to find the LCM of 36, 48, 21 and 28.

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

$48=2\times 2\times 2\times 2\times 3\times 3$

$21=3\times 7$

$28=2\times 2\times 7$

Thus the LCM of these numbers is $2^4\times 3^2\times 7=1008$
The LCM of 36, 48, 21 and 28 is 1008.

When 5 is added to 1008, we get 1013.
Hence, $1013$ is the least number when decreased by 5 is divisible by 36, 48, 21 and 28.