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.
What is the LCM of 4 and 10?
The LCM of 4 and 10 is 20 |
LCM of 4 and 10 by Multiples Method
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.