Question

The smallest square number exactly divisible by 2 4 6 is

Answer 1

Answer: 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.

Step-by-step explanation:

Answer 2

Given: Three numbers 2, 4 and 6

To find: The smallest square number exactly divisible by given numbers

Solution: To find the smallest square number exactly divisible by 2, 4 and 6, first we need to find least number which is exactly divisible by these i.e. LCM.

Using prime factorization method:

2 = 2 × 1

4 = 2 × 2 × 1

6 = 2 × 3 × 1

LCM is the product of maximum frequencies of all the factors of given numbers,

LCM = 2 × 2 × 3 = 12

The required number is a multiple of 12 which is a perfect square number.

Now, 12 × 3 = 36 (which is a square of 6)

Hence, the smallest square number exactly divisible by 2, 4 and 6 is 36.