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Question

Question 131

Solve the following question:

Find the smallest square number divisible by each of the numbers 8, 9 and 10.


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Solution

The least number divisible by each of the numbers 8, 9 and 10 is equal to the LCM of 8, 9 and 10
28,9,1024,9,522,9,531,9,531,3,551,1,51,1,1
LCM of 8, 9 and 10 =2×2×2×3×3×5=360
Prime factors of 360 =(2×2)×2×(3×3)×5
Here, prime factors 2 and 5 are unpaired. Clearly, to make it a perfect square, it must be multiplied by 2×5, ie. 10
Therefore, required number =360×10=3600
Hence, the smallest square number divisible by each of the numbers 8, 9 and 10 is 3600.


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