Question

find the smallest square number that is exactly divisible by 2 3 4 and 6​

Answer 1

Step-by-step explanation:

TO FIND:-

The smallest square number divisible by 2, 3, 4 and 6

UNDERSTANDING THE CONCEPT:-

The smallest square number exactly divisible by 2, 4, and 6 is the smallest multiple of the LCM of 2, 4, 6 such that this multiple is also a square number

STEPS:-

2 = 1 x 2

4 = 1 x 2 x 2

6 = 1 x 2 x 3

Therefore, L.C.M. of 2,4,6 is = 1 x 2 x 2 x 3 = 12

Integral multiples of 12 are

12, 24, 36, 48, 60, 72, 84, 96, 108, 120

CONCEPT REFRESHER:-

It is seen that 36 is the first multiple which is a square number (36= 6^2) and 36 is exactly divisible by 2,4, and 6.

PROVED:-

Hence 36 is the required number (Proved).