Question

Find the smallest square number which can be divisible by 4,12 and,16.

Answer 1

For any number to be exactly divisible by 4,12, and 16, that number has to be exactly divisible by the L.C.M. of those three numbers.

Now 4 = 2², 12 = 2² x 3
and 16=2²x2²

Therefore, L.C.M. of 4, 12 and 16 = 2² x 2² x 3 = 48

To find that number which is the smallest square number, we will take integral multiples of the L.C.M. and check for the squareness of each of the multiples so obtained at every step. The first number that will be a square will be the smallest square number.

48 x 1 = 48 (not a square)

48 x 2 = 96 (not a square)

48 x 3 = 144 (perfect square)

Therefore, since 144 is the square of 12, 144 is the smallest square number which is divisible by 4, 12, and 16