Answer 1

510 and 92

510 = 2 x 255

= 2 x 3 x 85

= 2 x 3 x 5 x 17

= 2 x 3 x 5 x 17 x 1

Therefore 510 = 2 x 3 x 5 x 17 x 1 .....(A)

92 = 2 x 46

= 2 x 2 x 23

Hence 92 = 2 x 2 x 23 .....(B)

From (A) and (B) HCF of 510 and 92 is = 2 and their 

LCM is 2 x 2 x 3 x 5 x 17 x 23 = 23460

Product of the LCM and HCF = 2 x 23460 = 46920

Product of the two numbers = 510 x 92 = 46920

Therefore it is proved that LCM x HCF = Product of the two numbers.