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Question

Find the least square number which is exactly divisible by 3,4,5,6 and 8.


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Solution

Calculate the LCM of given numbers

Given numbers are: 3,4,5,6 and 8. Their LCM is,

23456823253423153233153151151111111LCM3,4,5,6,8=2×2×2×3×5=120

To make it a perfect square, it must be multiplied by 2×3×5 to get pairs of prime factors.

So, 120×30=3600 is the least number which is exactly divisible by 3,4,5,6 and 8.

Hence, the required least square number is 3600.


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