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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

The least square number divisible by each of 3, 4, 5, 6 and 8 is equal to the LCM of 3, 4, 5, 6 and 8
23,4,5,6,823,2,5,3,423,1,5,3,233,1,5,3,151,1,5,1,11,1,1,1,1
LCM of 3, 4, 5, 6 and 8 =2×2×2×3×5=120
The prime factorisation of 120 =(2×2)×2×3×5
Here, prime factors 2, 3 and 5 are unpaired. Clearly, to make it a perfect square, it must be multiplied by 2×3×5 i.e. 30
Therefore, required number =120×30=3600
Hence, the least square number is 3600.

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