# Relationship between H.C.F. and L.C.M.

We will learn the relationship between H.C.F. and L.C.M. of two numbers.

First we need to find the highest common factor (H.C.F.) of 15 and 18 which is 3.

Then we need to find the lowest common multiple (L.C.M.) of 15 and 18 which is 90.

H.C.F. × L.C.M. = 3 × 90 = 270

Also 15 × 18 = 270

Therefore, product of H.C.F. and L.C.M. of 15 and 18 = product of 15 and 18.

So, from the above explanation we conclude that the product of highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of two numbers is equal to the product of two numbers

or, H.C.F. × L.C.M. = First number × Second number

or, L.C.M. = First number × Second number/ H.C.F.

Solved examples on the relationship between H.C.F. and L.C.M.:

1. Find the L.C.M. of 1683 and 1584.

First we find highest common factor of 1683 and 1584

Therefore, highest common factor of 1683 and 1584 = 99

Lowest common multiple of 1683 and 1584 = First number × Second number/ H.C.F.

= 1584 × 1683/99

= 26928

2. Highest common factor and lowest common multiple of two numbers are 18 and 1782 respectively. One number is 162, find the other.

We know, H.C.F. × L.C.M. = First number × Second number then we get,

18 × 1782 = 162 × Second number

18 × 1782/162 = Second number

Therefore, the second number = 198

3. The highest common factor and the lowest common multiple of two numbers are 825 and 25 respectively. If one of the two numbers is 275, find the other number.

We know, H.C.F. × L.C.M. = First number × Second number then we get,

825 × 25 = 275 × Second number

825 × 25/ 275 = Second number

Therefore, the second number = 75

To Find Lowest Common Multiple by using Division Method

Relationship between H.C.F. and L.C.M.

Worksheet on H.C.F. and L.C.M.

Word problems on H.C.F. and L.C.M.

Worksheet on word problems on H.C.F. and L.C.M.