Question

Find the LCM and HCF of the following pairs of integers and verify that LCM $\times$HCF = product of the two numbers.
(i) $336$ and $54$

Answer 1

(i) $26$ and $91$

Factor of $26=2\times 13\times 1$

Factor of $91=7\times 13\times 1$

HCF of $26$ and $91=13\times 1=13$

LCM of $26$ and $91=2\times 7\times 13=182$

LCM $\times$ HCF $=182\times 13=2366$

$26\times 91=2366$

So, LCM.HCF $=$ product of the two numbers $=26\times 91.$

Hence proved.

(ii) $510\times 92$

Factor of $510=2\times 3\times 5\times 17\times 1$

Factor of $92=2\times 2\times 23$

HCF of $510$ and $92=2\times 2=2$

LCM of $510$ and $92=2\times 2\times 3\times 5\times 17\times 23=23,460$

LCM $\times$ HCF $=23,460\times 2=46,920$

$510\times 92=46,920$

So, LCM.HCF $=$ product of the two numbers $=510\times 92.$

Hence proved.

(iii) $336$ and $54$

Factor of $336=2\times 2\times 2\times 2\times 7\times 3\times 1$

Factor of $54=2\times 3\times 3\times 3$

HCF of $336$ and $54=2\times 3=6$

LCM of $336$ and $54=2\times 3\times 2\times 2\times 2\times 7\times 3\times 3=3,024$

LCM $\times$ HCF $=3,024\times 6=18,144$

$366\times 54=18,144$

So, LCM.HCF = product of the two numbers $=336\times 54.$

Hence proved.