# Find the $\mathrm{LCM}$ and HCF of the following pairs of integers and verify that LCM $\times \mathrm{HCF}=$ product of two numbers.

Question.

Find the LCM and HCF of the following pairs of integers and verify that LCM $\times \mathrm{HCF}=$ product of two numbers.

(i) 26 and 91

(ii) 510 and 92

(iii) 336 and 54

Solution:

(i) 26 and 91

So, $26=2 \times 13$

So. $91=7 \times 13$

Therefore,

$\operatorname{LCM}(26,91)=2 \times 7 \times 13=182$

$\operatorname{HCF}(26,91)=13$

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

and $26 \times 91=2366$

i.e., $\mathrm{LCM} \times \mathrm{HCF}=$ product of two numbers.

(ii) 510 and 92

$510=2 \times 3 \times 5 \times 17,92=2^{2} \times 23$

$\operatorname{LCM}(510,92)=2^{2} \times 3 \times 5 \times 17 \times 23=23460$

$\mathrm{HCF}=(510,92)=2$

Verification :–

LCM $\times$ HCF $=23460 \times 2=46920$

and $510 \times 92=46920$

i.e., $\mathrm{LCM} \times \mathrm{HCF}=$ product of two numbers.

(iii) 336 and 54

$336=2^{4} \times 3 \times 7$

$54=2 \times 3^{3}$

$\mathrm{LCM}=2^{4} \times 3^{3} \times 7=3024$

$\mathrm{HCF}=2 \times 3=6$

Verfication,

LCM $\times$ HCF $=2^{4} \times 3^{3} \times 7 \times 2 \times 3=18144$

Product of two numbers $=336 \times 54=18144$

i.e., $\mathrm{LCM} \times \mathrm{HCF}=$ product of two numbers.