Question

The L.C.M of two numbers is six - times their HCF. If their difference between L.C.M and H.C.F is 60 and one of the two numbers is 36, find the other number.

• A. 14
• B. 18
• C. 22
• D. 24

Answer 1

The correct option is D 24

One number = 36 (given)
L.C.M of two numbers = 6 (H.C.F of two numbers) ----- (i)
L.C.M - H.C.F = 60 -------- (ii)
From (i)
6 H.C.F - H.C.F = 60
5 H.C.F = 60
H.C.F = $\frac{60}{5}$ = 12

L.C.M = 6 (H.C.F) = 6 $\times$ 12 = 72
H.C.F $\times$ L.C.M = Product of two numbers
12 $\times$ 72 = 36 $\times$ Second number
Second number = $\frac{12\times 72}{36}$
Second number = 24