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 $$ = 2520$$