Question

If a = 150 and b = 250, Find the H.C.F. and L.C.M of a and b. Also, show that the product of H.C.F and L.C.M is equal to product of a and b

Answer 1

The prime factorization of $150=2\times 3\times 5\times 5$
The prime factorization of $250=2\times 5\times 5\times 5$
$H.C.F=2\times 5\times 5=50$
$L.C.M=2\times 5\times 5\times 5\times 3=750$
The product of HCF and LCM = $50\times 750=37500$
Also, $a\times b=150\times 250=37500$
So the product of given numbers = product of HCF and LCM.