Question

Find the $LCM$ and $HCF$ of the pairs of integers $336$ and $54$ and verify that $LCM\times HCF=$ product of the two numbers.

Answer 1

By Prime factorization of numbers $336$ and $54$ we get,
$336=2\times 2\times 2\times 2\times 3\times 7=2^4\times 3\times 7$
$54=2\times 3\times 3\times 3=2\times 3^3$
For H.C.F, we find the minimum power of common prime factor.
H.C.F $=2\times 3=6$
For L.C.M. we find the highest power of the prime factor.
So, L.C.M $=2^4\times 3^3\times 7=16\times 27\times 7=3024$
Verification:
Product of both integers numbers $=336\times 54=18144$
H.C.F $\times$ L.C.M $=6\times 3024=18144$
So H.C.F $\times$ L.C.M = Product of both integers numbers