LCM of 15, 25, 40 and 75 is 600. LCM stands for Least Common Multiple or the Lowest common multiple also known as LCD Least Common Divisor is the positive integer that is a common multiple to the given set of numbers. Here the given set of numbers are 15, 25, 40 and 75. The smallest common multiple for all these numbers among many is 600, and hence it is the LCM. You can use HCF and LCM to differentiate between HCF and LCM.
What is LCM of 15, 25, 40 and 75
The Least Common Multiple or Lowest Common Multiple of 15, 25, 40 and 75 is 600.
How to Find LCM of 15, 25, 40 and 75?
LCM of 15, 25, 40 and 75 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 15, 25, 40 and 75 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 15, 25, 40 and 75 can be expressed as;
15 = 3 × 5
25 = 5 × 5
40 = 2 × 2 × 2 × 5
75 = 3 × 5 × 5
LCM (15, 25, 40, 75) = 2 × 2 × 2 × 3 × 5 × 5 = 600
LCM of 15, 25, 40 and 75 Using Division Method
In the Division Method, the given set of numbers are written in the same row separated by a comma. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left.
|
5 |
15 |
25 |
40 |
75 |
|
3 |
3 |
5 |
8 |
15 |
|
5 |
1 |
5 |
8 |
5 |
|
2 |
1 |
1 |
8 |
1 |
|
2 |
1 |
1 |
4 |
1 |
|
2 |
1 |
1 |
2 |
1 |
|
× |
1 |
1 |
1 |
1 |
No further division can be done as only prime numbers are left out.
LCM (15, 25, 40, 75) = 2 × 2 × 2 × 3 × 5 × 5 = 600
LCM of 15, 25, 40 and 75 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 15, 25, 40 and 75
Multiples of 15:
15, 30, 45, 60, 75, 90, …, 165, 180, 195, 210, …, 300, 315, 330, 345, .., 420, 435, 450, 465, … 555, 570, 585, 600, 615, 630…..
Multiples of 25:
25, 50, 75, …, 200, 225, 250, 275, …, 400, 425, 450, …, 550, 575, 600, 625, 650…
Multiples of 40:
45, 90, 135, …., 945, 990, 1035…,441, 1215, 600, 1305..
Multiples of 75:
75, 150, 225, 300, 375, 450, 525, 600, 675, 750…
LCM (15, 25, 40, 75) = 600
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 15, 25, 40 and 75?
Answer: 600 is the smallest number that is divisible by 15, 25, 40 and 75.
What is the LCM of 40 and 75?
Answer: LCM of 40 and 75 is 600.
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