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Question

What is the smallest square number that is divisible by 28,40,70?

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Solution

2|28,40,70
2|14,20,35
2| 7, 10,35
5| 7, 5,35
7| 7, 1, 7
1, 1, 1
Smallest number divisible by 28,40 and 70= L.C.M. of 28,40 and 70=2×2×2×5×7=280
So, the smallest perfect square which is divisible by 28,40 and 70 is (2×2×2×5×7)×2×5×7=280×2×5×7=19600.

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