Find the LCM and HCF of the following pairs of integers and verify that LCM * HCF = Product of the two numbers.

(1) 26 & 91

(2) 510 & 92

(3) 336 & 54

Sol. (1) Prime factors of 26 = 2 x 13

Prime factors of 91 = 7 x 13

Hence, HCF = Common factors between 26 and 91 = 13 and LCM=13x2x7=182

Now product of numbers 26 and 91

= 26 x 91 = 2366 and Product of HCF and LCM = 13 x 182 = 2366

So, it verify that product of two numbers = Product of HCF and LCM.

(2) Prime factors of 510 = 2 x 3 x 5 x 17

Prime factors of 92 = 2 x 2 x 23

Hence, HCF=2 and LCM=2*2*3 * 5*17*23 = 23460

Now product of Numbers 510 and 92 = 46920 and product of HCF and LCM = 2 x 23460 = 46920

Hence, verified that product of two numbers 18 equal to product of their HCF and LCM.

(3) Prime factors of336 = 2 x 2 x 2 x 2 x 3 x 7

Prime factors of 54 = 2 x 3 x 3 x 3

Hence, HCF (Product of common factors of 336 and 54)

=2 x 3=6

And LCM (Product of all common factors with remaining factors)

= (2 x 3) x 2 x 2 x 2 x 3 x 3 x 7=3024

Now, product of numbers 336 and 54 = 336 x 54 = 18144

and product of HCF and LCM = 6 x 3024 = 18144

Hence, product of two numbers: Product of HCF and LCM.