Question

What is the least perfect cube divisible by 2, 3, 4 and 6

Answer 1

36 is divisible by 2,3,4&6.

Also, 36 = 6²

Now, 36×6 = 216

Now, 6³ = 216 (perfect cube)

Divisible by 2,3,4&6

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Answer 2

Given: Four numbers 2, 3, 4 and 6

To find: The least perfect cube divisible by the given numbers

Solution: To find the required number, first we need to find the least number which is exactly divisible by 2, 3, 4 and 6 i.e., their LCM.

Using prime factorization method:

2 = 2 × 1

3 = 3 × 1

4 = 2 × 2 × 1

6 = 2 × 3 × 1

LCM is the product of maximum frequencies (maximum frequency of a number occuring as prime factors of any one given number) of all the factors.

LCM = 2 × 2 × 3 = 12 (2 occuring maximum two times as factors of 4 and 3 occuring maximum one time as factor of 3 and 6)

So, 12 is the least number which is exactly divisible by 2, 3, 4 and 6.

The required least perfect cube is a multiple of 12 which is a perfect cube number.

We get, 12 × 18 = 216 (which is a cube of 6)

Hence, the least perfect cube divisible by 2, 3, 4 and 6 is 216.