Question

(i) Find the H.C.F. of 90 and 162.
(ii) Find the L.C.M. of 90 and 162.
(iii) What is the product of HCF and LCM of 90 and 162?

Answer 1

(i) The prime factorization of $90=2\times 3\times 3\times 5$
The prime factorization of $162=2\times 3\times 3\times 3\times 3$
$HCF=2\times 3\times 3=18$
(ii) The prime factorization of $90=2\times 3\times 3\times 5$
The prime factorization of $162=2\times 3\times 3\times 3\times 3$
$LCM=2\times 3\times 3\times 3\times 3\times 5=810$
(iii) The product of HCF and LCM $=18\times 810=14580$
We can also note that $14580=90\times 162$.
So the product of given numbers = product of HCF and LCM.