LCM of 60 and 120 is 120. The Least Common Divisor (LCD) also known as Least Common Multiple or Lowest Common Multiple simply known as LCM is the least positive integer that is divisible by the given numbers. In the given set of numbers 60 and 120, 120 is the first(least or smallest) number that is common in the set of multiples of 60 and 120. You can refer to LCM with Examples for better understanding.
What is LCM of 60 and 120
The Least Common Multiple or Lowest Common Multiple of 60 and 120 is 120.
How to Find LCM of 60 and 120?
LCM of 60 and 120 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 60 and 120 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 60 and 120 can be expressed as;
60 = 2 × 2 × 3 × 5
120 = 2 × 2 × 2 × 3 × 5
Since 60 is the factor of 120, the LCM is the product of 60 and 2 as the prime factors of 60 are the same as the prime factors of 120 along with 2.
Therefore, LCM (60, 120) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 60 and 120 Using Division Method
In the Division Method, the numbers 60 and 120 are divided by prime divisors and the product of prime divisors forms the LCM.
|
2 |
60 |
120 |
|
2 |
30 |
60 |
|
2 |
15 |
30 |
|
3 |
15 |
15 |
|
5 |
5 |
5 |
|
× |
1 |
1 |
LCM (60, 120) = 2 × 2 × 2 × 3 × 5 = 120
LCM of 60 and 120 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 60 and 120.
|
Multiples of 60 |
Multiples of 120 |
|
60 |
120 |
|
120 |
240 |
|
180 |
360 |
LCM (60, 120) = 120
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 60 and 120?
Answer: 120 is the smallest number that is divisible by both 60 and 120.
What is the LCM for 2, 3, 4, 60 and 120?
Answer: LCM for 2, 3, 4, 60 and 120 is 120 as 2, 3, 4 are the factors of both 60 and 120.
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