find the smallest square number divisible by each one of the number 8,9 and 10
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L.C.M. of 8,9,10 is 2*2*2*3*3*5=360.
Since 2 and 5 are not in pairs multiply by 2 and 5 to make it a perfect square. The required number=360*2*5=3600.
Since 2 and 5 are not in pairs multiply by 2 and 5 to make it a perfect square. The required number=360*2*5=3600.
Answered by
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Answer:
Smallest Square number is 3600.
Step-by-step explanation:
To find: Smallest Square number divisible by 8 , 9 , 10
Prime Factorization to find LCM,
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
LCM ( 8 , 9 , 10 ) = 2 × 2 × 2 × 3 × 3 × 5 = 360
Clearly 360 but it is not a perfect square number.
Now we make the pairs complete by multiplying same numbers in prime factorization of LCM.
We need one 2 and one 5 to complete the pair.
We get, Least Square number = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 3600
Therefore, Smallest Square Number is 3600.
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