LCM of 40, 56 and 60 is 840. Let us consider the list of common multiples of 40, 56 and 60. They are 840, 1680, 2520 and so on. The first common multiple is 840 which is lesser than the other multiples. Hence 840 becomes the LCM of 40, 56 and 60. The LCM and LCD whose full form is Lowest/Least Common Multiple and Least Common Divisor respectively is the smallest common multiple of given numbers. You can read more on LCM for details.
What is LCM of 40, 56 and 60
The Least Common Multiple or Lowest Common Multiple of 40, 56 and 60 is 840.
How to Find LCM of 40, 56 and 60?
LCM of 40, 56 and 60 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 40, 56 and 60 Using Prime Factorisation Method
In the Prime Factorisation method, 40, 56 and 60 can be expressed as;
40 = 2 × 2 × 2 × 5
56 = 2 × 2 × 2 × 7
60 = 2 × 2 × 3 × 5
The product of common factors and non-common factors will be the LCM.
Therefore, LCM (40, 56, 60) = 2 × 2 × 2 × 3 × 7 × 5 = 840
LCM of 40, 56 and 60 Using Division Method
In the Division Method, 40, 56 and 60 are all divided together by the same common prime factors starting from the smallest divisor. The division is progressed by increasing the prime divisors and till the remainders become one. Product of prime divisors forms the LCM.
|
2 |
40 |
56 |
60 |
|
2 |
20 |
28 |
30 |
|
2 |
10 |
14 |
15 |
|
3 |
5 |
7 |
15 |
|
5 |
5 |
7 |
5 |
|
7 |
1 |
7 |
1 |
|
× |
1 |
1 |
1 |
LCM (40, 56, 60) = 2 × 2 × 2 × 3 × 5 × 7 = 840
LCM of 40, 56 and 60 Using Listing the Multiples
By listing all the multiples of 40, 56 and 60, we can identify the smallest common multiple, which is the LCM. Below is the list of multiples for 40, 56 and 60
Multiples of 40
40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600, 640, 680, 720, 760, 800, 840, 880, 920
Multiples of 56
56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, 728, 784, 840, 896, 952
Multiples of 60
60, 120, 180, 240, 300, 360, 420, 480, 540, 600, 660, 720, 780, 840, 900, 960
LCM (40, 56, 60) = 840
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 40, 56 and 60?
Answer: 840 is the smallest number that is divisible by both 40, 56 and 60.
What is the LCM for 20, 40, 56 and 60?
Answer: LCM for 20, 40, 56 and 60 is 840.
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