Find the smallest square number that is divisible by each of the numbers 4 , 9 and 10

we know that the number that will be perfectly divisible by each one of 4 ,  9, and 10 is their LCM.

The LCM of these numbers is:

LCM of 4 , 9 , 10 = 2 × 2 × 3 × 3 ×  5 = 180

Here, prime factor 5 does not have its pair

There fore, 180 is not a perfect square.

If we multiply 180 with 5, then the number will be comeape rfect square.

There fore, 180 should be multiplied with 5 to obtain a perfect square.

Hence,

There quireds quare number is 180 ×  5 = 900