Find the LCM and HCF of the following pairs of integers and verify that
Question:

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = Product of the integers:

(i) 26 and 91

(ii) 510 and 92

(iii) 336 and 54

Solution:

TO FIND: LCM and HCF of following pairs of integers

TO VERIFY: L.C.M $\times$ H.C.F $=$ product of the numbers

(i) 26 and 91

Let us first find the factors of 26 and 91

$26=2 \times 13$

$91=7 \times 13$

L.C.M of 26 , and $91=2 \times 7 \times 13$

L.C.M of 26, and $91=182$

H.C.F of 26, and $91=13$

We know that,

L. C. $M \times H .$ C. $F=$ First number $\times$ Second number

$\Rightarrow 182 \times 13=26 \times 91$

$\Rightarrow 2366=2366$

Hence verified

(ii) 510 and 92

Let us first find the factors of 510 and 92

$510=2 \times 3 \times 5 \times 17$

$92=2^{2} \times 23$

L.C.M of 510 and $92=2^{2} \times 3 \times 5 \times 23 \times 17$

L.C.M of 510 and $92=23460$

H.C.F of 510 and $92=2$

We know that,

L.C.M $\times$ H.C.F $=$ First Number $\times$ Second Number

$23460 \times 2=510 \times 92$

$46920=46920$

Hence verified

(iii) 336 and 54

Let us first find the factors of 336 and 54

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

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

L.C.M of 336 and $54=2^{4} \times 3^{3} \times 7$

L.C.M of 336 and $54=3024$

H.C.F of 336 and $54=6$

We know that,

L.C.M $\times$ H.C.F $=$ First Number $\times$ Second Nuber

$3024 \times 6=336 \times 54$

$18144=18144$

Hence verified