# LCM of 4 and 10

Common Multiple: When two or more numbers have the same numbers as their multiples, those multiples are said to be common multiples.

Least Common Multiple (LCM): The Least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of those numbers.

## LCM of 4 and 10 by MultiplesMethod

Find the least common Multiple (LCM) of 4 and 10.

Step 1: List the multiples of all the given numbers.

Multiples of 4

4 x 1 = 4
4 x 2 = 8
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
4 x 6 = 24

Multiples of 4 are 4, 8, 12, 16, 20, 24…

Multiples of 10

10 x 1 = 10
10 x 2 = 20
10 x 3 = 30
10 x 4 = 40
10 x 5 = 50
10 x 6 = 60

Multiples of 10 are 10, 20, 30, 40, 50, 60…

Step 2: Identify the common multiples of all the given numbers.

Common multiples of 4 and 10 are 20…

Step 3: Write the least common multiple (LCM) of all the given numbers.

Least Common Multiple (LCM) = 20 (the smallest number of the common multiples)

## LCM of 4 and 10 by Division Method

``````
2 | 4,  10
--|---------
2 | 2,   5
--|---------
5 | 1,   5
--|---------
| 1,   1``````

Least Common Multiple (LCM) = 2 x 2 x 5
LCM = 20

## LCM of 4 and 10 by Prime Factorisation Method

Step 1: Find the prime factorization of 4

``````  2 | 4
--|----
2 | 2
--|----
| 1``````

prime factorization of 4 = 2 x 2

Step 2: Find the prime factorization of 10

``````  2 | 10
--|-----
5 |  5
--|-----
|  1``````

prime factorization of 10 = 2 x 5

Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM

4 = 2 x 2

10 = 2 x 5

LCM = 2 x 2 x 5
LCM = 20

Hence, the LCM of 4 and 10 by prime factorization is 20.

Categories LCM