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.
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
Prime Factorization and Division Method for LCM and HCF
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
What is the LCM of 45 and 75?
Is the LCM of 45 and 75 the same as the HCF of 45 and 75?
Is 275 the LCM of 45 and 75?
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
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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