LCM of 45 and 75

LCM of 45 and 75 is 225. In Mathematics, the full form of LCM is Least Common Multiple. A method to find the smallest common multiple between any two or more numbers is defined as LCM. Students understand the concept of LCM in a precise manner by referring to the article LCM of Two Numbers, designed by professional teachers with utmost care. This article is the perfect guide for students who are in search of study material for effective exam preparation. Let us have a look at how to find the least common multiple of 45 and 75 in this article.

What is LCM of 45 and 75?

The Least Common Multiple of 45 and 75 is 225.

lcm of 45 and 75

How to Find LCM of 45 and 75?

The LCM of 45 and 75 can be determined by using the following methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 45 and 75 Using Prime Factorisation Method

By prime factorisation method, we can write 45 and 75 as the product of prime numbers, such that;

45 = 3 × 3 × 5

75 = 3 × 5 × 5

LCM (45, 75) = 3 × 3 × 5 × 5 = 225

LCM of 45 and 75 Using Division Method

In the division method, we divide the numbers 45 and 75 by their prime factors until we get the result as one in the complete row to calculate their LCM. The product of these divisors represents the least common multiple of 45 and 75. This can be done as below.

3 45 75
3 15 25
5 5 25
5 1 5
x 1 1

No more further division can be done.

Hence, LCM (45, 75) = 3 × 3 × 5 × 5 = 225

LCM of 45 and 75 Using Listing the Multiples

In listing the multiples method, we can find the LCM of 45 and 75 by writing the multiples of 45 and 75. The below table shows the multiples of 45 and 75.

 

Multiples of 45 Multiples of 75
45 75
90 150
135 225
180 300
225 375
270 450

LCM (45, 75) = 225

Related Articles

Least Common Multiple (LCM)

HCF and LCM

Prime Factorization and Division Method for LCM and HCF

LCM Calculator

LCM with Examples

LCM Formula

Video Lesson on Applications of LCM

Solved Examples 

Q. 1: What is the smallest number that is divisible by both 45 and 75?

Solution: 225 is the smallest number that is divisible by both 45 and 75.

 

Q. 2: The GCD and LCM of the two numbers are 15 and 225 respectively. If one number is 75, calculate the other number.

Solution: Let the other number be q

We know that,

GCD × LCM = 75 × q

q = (GCD × LCM) / 75

q = (15 × 225) / 75

q = 45

Hence the other number is 45.

Frequently Asked Questions on LCM of 45 and 75

Q1

What is the LCM of 45 and 75?

The LCM of 45 and 75 is 225.
Q2

Is the LCM of 45 and 75 the same as the HCF of 45 and 75?

No. LCM of 45 and 75 is 225 and HCF of 45 and 75 is 15.
Q3

Is 275 the LCM of 45 and 75?

No. The LCM of 45 and 75 is 225.
Q4

What is the GCF if the LCM of 45 and 75 is 225?

LCM × GCF = 45 × 75

Given

LCM = 225

225 × GCF = 45 × 75

GCF = 15

Q5

Mention the methods used to find the LCM of 45 and 75.

The methods used to find the LCM of 45 and 75 are

Prime Factorisation

Division Method

Listing the Multiples

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