Question

Lcm and hcf of two numbers are 360 and 5. find the number of such possible pairs.

Answer 1

LCM of two numbers is 360 = 2×2×2×3×3×5

HCF of the same numbers is 5
HCF is common for both two numbers i.e 5 comes in both numbers

so, possible pair is 5 and 360

Answer 2

Given:

L.C.M. of two numbers=360

H.C.F. of two numbers=5

To find:

The number of such possible pairs

Solution:

We can find the number of pairs by following the steps given below-

We know that the product of two numbers is equal to the product of their LCM and HCF.

Let the two numbers that are also co-primes be 5a and 5b.

So, Product of a and b= Product of LCM and HCF

5a×5b=360×5

ab=72

The possible pairs of numbers will be the ones that are co-primes.

The pairs of co-primes are (1, 72) and (8,9).

The possible pairs of numbers are (5, 360) and (45, 40).

Therefore, the number of such possible pairs is 2.