Question

the H.C.F of two numbers is 12 .if one number is four times the H.C.F and the other is five times the H.C.F then find the L.C.M of these numbers ​

Answer 1

Let the 2 numbers be (x, y)

Given:

H.C.F (x, y) = 12

x = 4 × H.C.F →→→→→ (Equation 1)

y = 5 × H.C.F →→→→→ (Equation 2)

To Find:

L.C.M (x, y) = ?

Method:

We know that;

Product of 2 numbers = H.C.F × L.C.M

⇒ xy = 12 × L.C.M

From Equation 1:

x = 4 × H.C.F = 4 × 12 = 48

⇒ x = 48

From Equation 2:

y = 5 × H.C.F = 5 × 12 = 60

⇒ y = 60

Product of 2 numbers = H.C.F × L.C.M

x × y = H.C.F × L.C.M

48 × 60 = 12 × L.C.M

⇒ L.C.M = $\dfrac{48 X 60}{12}$

⇒ L.C.M = 240

L.C.M of 48 and 60 is 240