Lcm of 15 and 25

Introduction to lcm of 15 and 25:

In this article let us learn what is lcm, what it stands for, what is the role of factor and multiple in finding lcm of 15 and 25 and how to find the lcm of any two numbers.

LCM stands for Least Common Multiple

Factor:

Let us learn what is factor through an example.Consider the number 15

15 is divisible by 3 and leaves remainder 0.

15 is divisible by 5 and leaves remainder 0.

So we could say that 3 and 5 are the factors of 15.

Factor of any number will lie between 1 and the number and obviously 1 and the number are also factors of the number. According to our example, 1 and 15 are factors of 15.

We can conclude that the divisor that exactly divides the dividend is called as factor. The word "exactly divides" mean when the dividend is divided by the divisor, the remainder should be zero.

Multiple:

Let us learn what is a multiple through an example. Let us consider a number  25.

25 is divisible by 5 and leaves remainder 0

Therefore, 25 is a multiple of 5 and 5 is a factor of 25.

Let us find the factors of some numbers say 12, 18

Consider 12

12 is divisible by 2 and leaves remainder 0

12 is divisible by 3 and leaves remainder 0

12 is divisible by 4 and leaves remainder 0

12 is divisible by 6 and leaves remainder 0

Therefore, 12 is a multiple of 2, 3, 4 and 6.

2, 3, 4 and 6 are the factors of 12.

Consider 18

18 is divisible by 2 and leaves remainder 0

18 is divisible by 3 and leaves remainder 0

18 is divisible by 6 and leaves remainder 0

18 is divisible by 9 and leaves remainder 0

Therefore, 18 is a multiple of 2, 3, 6 and 9.

2, 3, 6  and 9 are the factors of 18.

Finding Lcm of 15 and 25:

What is common multiple:

Consider number 100

100 is divisible by 2 and leaves remainder 0

100 is divisible by 4 and leaves remainder 0

100 is divisible by 5 and leaves remainder 0

100 is divisible by 10 and leaves remainder 0

100 is divisible by 20 and leaves remainder 0

100 is divisible by 25 and leaves remainder 0

100 is divisible by 50 and leaves remainder 0

Let us list out the factors of 100. They are 2, 4, 10, 20, 25, 50. So, 100 is a multiple of 2, 4, 10, 20, 25, 50.

Meaning of Least common multiple:

Let us take these two numbers 6 and 18

Multiples of 6 are  6, 12, 18, 24, 30, 36, 42, 48, 54,....

Multiples of 18 are 18, 36, 54, 72, ...

The common multiples of 6 and 18 are 18 and 54. But the least number between 18 and 54 is 18. So lcm of 6 and 18 is 18.

Note:

Here, between 6 and 18 18 is the bigger number and 18 is the multiple of 6. So, lcm of 6 and 18 is 18. In the given numbers if the greater number is a multiple of the least number, then the lcm between the two numbers is the greater number.
Consider any two numbers which are relatively prime, say 12 and 13. Lcm of 12 and 13 is their product. Lcm of 12 and 13 is 156. I like to share this math help free online tutor with you all through my article.

Working Solution for Lcm of 15 and 25:

Reading the above notes, we could say that 25 is not the lcm of 15 and 15 since 25 is not a multiple of 15 and 15 and 25 are not relatively prime.

Let us write the multiples of 15 and 25.

Multiples of 15 are 15, 30, 45, 60, 75, 80,...

Multiples of 25 are 25, 50, 75, 100,...

Pick out the least common multiple from teh above multiples of 15 and 25.

It is 75. So, lcm of 15 and 25 is 75.