Question

Find the HCF and LCM of the following integers by applying the prime factorization method
$40,36$ and $126$

Answer 1

$40=2\times 2\times 2\times 5=2^3\times 5$
$36=2\times 2\times 3\times 3=2^2\times 3^2$
and $126=2\times 3\times 3\times 7=2\times 3^2\times 7$
For H.C.F taking minimum power of common factor
H.C.F $=(2{)}^1=2$
For L.C.M, taking maximum power of prime factors
L.C.M $=2^3\times 3^2\times 5\times 7=8\times 9\times 5\times 7=2520$
Hence, H.C.F $=2$
L.C.M $=2520$