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Find the smallest square number that is divisible by each of the numbers 5, 15 and 45.
Given: 5, 15, 45
To find: We need to find the smallest square number that is divisible by each of the no 5, 15, and 45.
Solution:
First we need to find the LCM of the given numbers i.e. 5, 15 and 45.
Now,
Writing all the numbers as a product of their prime factors:
Prime factorization of 5:
- 5 = 51
Prime factorization of 15:
- 3 $\times $ 5 = 31 $\times $ 51
Prime factorization of 45:
- 3 $\times $ 3 $\times $ 5 = 32 $\times $ 51
Highest power of each prime number:
- 32 , 51
Multiplying these values together:
- 32 $\times $ 51 = 45
Thus,
LCM(5, 15, 45) = 45
We know that in a perfect square all the prime factors of that number are in pairs. So, we need to multiply 45 with 5 to make it a perfect square.
45 $\times $ 5 = 225
So, the smallest square number that is divisible by each of the no 5, 15 and 45 is 225.
Updated on: 10-Oct-2022
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