Find the HCF and LCM of the integers 12,15,an | vedclass

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(A) To find the $HCF$ and $LCM$ of $12$,$15$,and $21$ using prime factorization:Step $1$: Write the prime factorization of each number.$12 = 2^2 	ime

Vedclass · Accepted Answer

$HCF = 3, LCM = 420$

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(A) To find the $HCF$ and $LCM$ of $12$,$15$,and $21$ using prime factorization:Step $1$: Write the prime factorization of each number.$12 = 2^2 	imes 3^1$$15 = 3^1 	imes 5^1$$21 = 3^1 	imes 7^1$Step $2$: Find the $HCF$ (Highest Common Factor).The $HCF$ is the product of the smallest power of each common prime factor.The only common prime factor is $3$,and its smallest power is $3^1$.Therefore,$HCF = 3$.Step $3$: Find the $LCM$ (Least Common Multiple).The $LCM$ is the product of the greatest power of each prime factor involved.The prime factors involved are $2, 3, 5,$ and $7$.The greatest powers are $2^2, 3^1, 5^1,$ and $7^1$.$LCM = 2^2 	imes 3^1 	imes 5^1 	imes 7^1 = 4 	imes 3 	imes 5 	imes 7 = 420$.Thus,$HCF = 3$ and $LCM = 420$.

Find the $HCF$ and $LCM$ of the integers $12$,$15$,and $21$ by the prime factorization method.

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