Question

.

If two positive integers ‘p’ and ‘q’ are written as p = a4b5

and q = a2b where a, b are prime

numbers then find HCF of (p, q).​

Answer 1

$\bf p=a {}^{2} b {}^{3} \\ \bf p = a.a.b.b.b \\ \bf q=a {}^{3} b \\ \bf q=a.a.a.b \\ \bf H.C.F (p,q) = a.a.b \\ \bf H.C.F (p,q) = a b \\ \bf L.C.M (p,q) = a.a.a.b.b.b \\ \bf L.C.M (p,q) = a {}^{2} b {}^{3} \\ \bf we \: prove \: that, \\ \bf L.C.M \: (p,q) \: \times \: H.C.F \: (p,q) = p q \\ \bf L.H.S = L.C.M (p,q) \times H.C.F (p,q) \\ \bf L.H.S = (a {}^{3} b {}^{3} ) \times (a {}^{2} b) \\ \bf L.H.S = a {}^{5} b {}^{4} \\ \bf R.H.S = (a {}^{2} b {}^{3} ) \times (a {}^{3} b) \\ \bf R.H.S = a {}^{5} {b}^{4}$