LCM of 24, 40, 80 and 120 is 240. LCM is an abbreviated version of Least Common Multiple or Lowest Common Multiple. Lowest meaning first or smallest or least, Common meaning same at different instances and Multiple meaning a number obtained by multiplying by 2 numbers. So LCM means a smallest number that is common to the list of multiples. Consider the example for finding the LCM of 24, 40, 80 and 120. The answer is 240. 240 is the least number that is commonly divisible by 24, 40, 80 and 120. You can use the HCF and LCM to understand LCM along with HCF.
What is LCM of 24, 40, 80 and 120
The Least Common Multiple or Lowest Common Multiple of 24, 40, 80 and 120 is 240.
How to Find LCM of 24, 40, 80 and 120?
LCM of 24, 40, 80 and 120 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24, 40, 80 and 120 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 24, 40, 80 and 120 can be expressed as;
24 = 2 × 2 × 2 × 3
40 = 2 × 2 × 2 × 5
80 = 2 × 2 × 2 × 2 × 5
120 = 2 × 2 × 2 × 3 × 5
LCM (24, 40, 80, 120) = 2 × 2 × 2 × 2 × 3 × 5 = 240
LCM of 24, 40, 80 and 120 Using Division Method
In the Division Method,
- Divide all given numbers with 2.
- Continue division even if 1 number is also divisible by 2
- If no division is possible, then divide with 3 or 5 or other prime numbers.
- The division will be stopped when no further division is possible. i,e the remainders are 1
- The product of the divisors form the LCM.
|
2 |
24 |
40 |
80 |
120 |
|
2 |
12 |
20 |
40 |
60 |
|
2 |
6 |
10 |
20 |
30 |
|
2 |
3 |
5 |
10 |
15 |
|
3 |
3 |
5 |
5 |
15 |
|
5 |
1 |
5 |
5 |
5 |
|
× |
1 |
1 |
1 |
1 |
LCM (24, 40, 80, 120) = 2 × 2 × 2 × 2 × 3 × 5 = 240
LCM of 24, 40, 80 and 120 Using Listing the Multiples
List the multiples of 24, 40, 80 and 120.
The first multiple which is 240 becomes the LCM.
Multiples of 24:
24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288…
Multiples of 40:
40, 80, 120, 160, 200, 240, 280, 320
Multiples of 80:
80, 160, 240, 320, 400…
Multiples of 120:
120, 240, 360, 480…
LCM (24, 40, 80, 120) = 240
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 24, 40, 80 and 120?
Answer: 240 is the smallest number that is divisible by 24, 40, 80 and 120.
What is the LCM of 10, 12, 24, 40, 80 and 120?
Answer: LCM of 10, 12, 24, 40, 80 and 120 is 240.
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