Question

How many pairs of numbers are possible whose LCM is 280 and HCF is 7?

Answer 1

Let the no.be 7x & 7y

Where x & y are co-primes___(1)

Product of two numbers=product of their HCF & LCM

i.e. 7x X 7y =7 X 280

i.e.  xy=40_____(2)

40=2 X 2 X 2 X 5 X 1

Therefore,values of ‘x’ & ‘y’ which satisfies (1) & (2) are

8,5

1,40

Therefore,numbers(7x & 7y) are

56,35

7,280

Thus,2 pairs of numbers are possible.