LEAST COMMON MULTIPLE BY DIVISION METHOD

Least common multiple is the smallest number which is a multiple of the given numbers.

For example, consider the numbers 4 and 5.

The whole numbers which are multiples of both both 4 and 5 are

20, 40, 60, 80, ..........

All the above numbers are multiples of both 4 and 5.

Can we get a whole number less than 20 which is a multiple of both 4 and 5?

NO, we CAN'T.

So, 20 is the smallest whole number which is a multiple of both 4 and 5.

In other words, 20 is the smallest whole number which is evenly divisible by both 4 and 5.

Therefore, 20 is the least common multiple of 4 and 5.

More Examples :

Least common multiple of 2 and 3 = 6

Least common multiple of 4 and 6 = 12

Least common multiple of 3 and 6 = 6

Example 1 :

Find the least common multiple of 24 and 60.

Solution :

Using L division, divide both the numbers by a common divisor. Continue this process, until you get a common divisor for both the numbers.

The least common multiple of 24 and 60 is

= 2 x 2 x 3 x 2 x 5

= 120

Example 2 :

Find the least common multiple of 48, 72 and 108.

Solution :

Using L division, divide the given numbers by a common divisor. Continue this process, until you get a common divisor at least for any of the two numbers.

The least common multiple of 48, 72 and 108 is

= 2 x 2 x 3 x 2 x 3 x 2 x 1 x 3

= 432

Solved Problems

In each case, find the least common multiple of the numbers by division method.

Problem 1 :

4 and 6

Solution :

Using L division, divide both the numbers by a common divisor. Continue this process, until you get a common divisor for both the numbers.

The least common multiple of 4 and 6 is

= 2 x 2 x 3

= 12

Problem 2 :

2 and 3

Solution :

There is no common divisor for both 2 and 3 other than 1.

So, the least common multiple of 2 and 3 is

= 2 x 3

= 6

Problem 3 :

4 and 5

Solution :

There is no common divisor for both 4 and 5 other than 1.

So, the least common multiple of 4 and 5 is

= 4 x 5

= 20

Problem 4 :

3 and 6

Solution :

Using L division, divide both the numbers by a common divisor. Continue this process, until you get a common divisor for both the numbers.

The least common multiple of 4 and 6 is

= 3 x 1 x 2

= 6

Problem 5 :

12 and 18

Solution :

Using L division, divide both the numbers by a common divisor. Continue this process, until you get a common divisor for both the numbers.

The least common multiple of 12 and 18 is

= 2 x 3 x 2 x 3

= 36

Problem 6 :

4, 5 and 8

Solution :

Using L division, divide the given numbers by a common divisor. Continue this process, until you get a common divisor at least for any of the two numbers.

The least common multiple of 4, 5 and 8 is

= 2 x 2 x 1 x 5 x 2

= 40

Problem 7 :

4, 6, 8 and 12

Solution :

Using L division, divide the given numbers by a common divisor. Continue this process, until you get a common divisor at least for any of the two numbers.

The least common multiple of 4, 6, 8 and 12 is

= 2 x 2 x 3 x 1 x 1 x 2 x 1

= 24

Problem 8 :

2, 3, 4 and 5

Solution :

Using L division, divide the given numbers by a common divisor. Continue this process, until you get a common divisor at least for any of the two numbers.

The least common multiple of 2, 3, 4 and 5 is

= 2 x 1 x 3 x 2 x 5

= 60

Problem 9 :

2, 4, 5 and 8

Solution :

Using L division, divide the given numbers by a common divisor. Continue this process, until you get a common divisor at least for any of the two numbers.

The least common multiple of 2, 4, 5 and 8 is

= 2 x 2 x 1 x 1 x 5 x 2

= 40

Problem 10 :

3, 6, 7 and 14

Solution :

Using L division, divide the given numbers by a common divisor. Continue this process, until you get a common divisor at least for any of the two numbers.

The least common multiple of 3, 6, 7 and 14 is

= 3 x 7 x 2 x 1 x 1 x 1 x 1

= 42

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