LCM of 15 25 40 and 75

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.

lcm of 15 25 40 and 75

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.

Frequently Asked Questions on LCM of 15, 25, 40 and 75

Q1

What is the LCM of 15, 25, 40 and 75?

The LCM of 15, 25, 40 and 75 is 600.
Q2

What is the difference between the LCM 15, 25, 40 and 75 and the Highest Common Factor of 15, 25, 40 and 75?

The Least Common Multiple of 15, 25, 40 and 75 is 600 and the Highest Common Factor of 15, 25, 40 and 75 is 5.
Q3

Is the LCM and LCD both the same for 15, 25, 40 and 75?

Yes. The Least Common Multiple and Least Common Divisor are both the same for 15, 25, 40 and 75  which is 600.
Q4

What are the first 3 common multiples of 15, 25, 40 and 75?

The first three common multiples of 15, 25, 40 and 75 are 600, 1200, and 1800.
Q5

Is the LCM of 15 and 40 same as the LCM of 25 and 75?

No. LCM of 15 and 40 is 120, whereas the LCM of 25 and 75 is 75. They are not the same.

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