Question

The HCF and LCM of two numbers are 8 and 480 respectively.If one number is 40, find the other. *

Answer 1

• The other number = 96.

Given :–

• Thd highest common factor (H.C.F.) = 8.
• The least common multiple (L.C.M.) = 480.
• One number = 40.

To Find :–

• The other number.

Solution :–

Let,

The other number be x.

We know that,

L.C.M. × H.C.F. = Product of two numbers

I.e.,

L.C.M. × H.C.F. = One number × Other number

We have,

• L.C.M. = 480.
• H.C.F. = 8.
• One number = 40.

Now,

Substitute all the given values.

$\hookrightarrow480 \times 8 = 40 \times x$

$\hookrightarrow3840 = 40x$

$\hookrightarrow \dfrac{384 \cancel0}{4 \cancel0} = x$

$\hookrightarrow \cancel \dfrac{384}{4} = x$

$\hookrightarrow96 = x$

Hence,

The other number is 96.

Verification :–

L.C.M. × H.C.F. = Product of two numbers

We have,

• L.C.M. = 480.
• H.C.F. = 8.
• One number = 40.
• Other number = 96.

$\hookrightarrow 480 \times 8 = 40 \times 96$

$\hookrightarrow 3840 = 3840$

Hence Verified !!