Find the least square number which is divisible by 4,8,2,6 and 12?

First, find the Least Common Multiple (LCM) of 4,8,2,6, and 12.
Prime factorization:

2=2
1


4=2
2


6=2
1
×3
1


8=2
3


12=2
2
×3
1


LCM=2
3
×3
1
=8×3=24
To find the least perfect square that is a multiple of 24, we need to pair the prime factors:

24=2×2×2×3=2
2
×2
1
×3
1

To make it a perfect square, we must multiply by 2×3=6:

Least Square Number=24×6=144