Find the HCF and LCM of the integers 336 and | vedclass

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(A) Step $1$: Prime factorization of $336$ and $54$.$336 = 2^4 	imes 3^1 	imes 7^1$$54 = 2^1 	imes 3^3$Step $2$: Find $HCF$.$HCF = 2^{\min(4,1)}

Vedclass · Accepted Answer

$HCF = 6, LCM = 3024; 18144 = 18144$

Vedclass · Answer

(A) Step $1$: Prime factorization of $336$ and $54$.$336 = 2^4 	imes 3^1 	imes 7^1$$54 = 2^1 	imes 3^3$Step $2$: Find $HCF$.$HCF = 2^{\min(4,1)} 	imes 3^{\min(1,3)} = 2^1 	imes 3^1 = 6$.Step $3$: Find $LCM$.$LCM = 2^{\max(4,1)} 	imes 3^{\max(1,3)} 	imes 7^1 = 2^4 	imes 3^3 	imes 7 = 16 	imes 27 	imes 7 = 3024$.Step $4$: Verify $HCF 	imes LCM = 	ext{Product of integers}$.$HCF 	imes LCM = 6 	imes 3024 = 18144$.$	ext{Product of integers} = 336 	imes 54 = 18144$.Since $18144 = 18144$, the relationship is verified.

Find the $HCF$ and $LCM$ of the integers $336$ and $54$ and verify that $HCF \times LCM = \text{product of the two integers}$.

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