Find the least square number which is exactly divisible by

Question:

Find the least square number which is exactly divisible by each of the numbers 8, 12, 15 and 20.

Solution:

The smallest number divisible by each of these numbers is their L.C.M.

L.C.M. of 8, 12, 15, 20 = 120

Resolving into prime factors: 

$120=2 \times 2 \times 2 \times 3 \times 5$

To make this into a perfect square, we need to multiply the number with $2 \times 3 \times 5=30$.

Required number $=120 \times 30=3600$

 

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