LCM of 45 and 50 is 450. The least common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. Students who want to gain proficiency in calculating the highest common factor and least common factor of given numbers are advised to follow the article HCF and LCM curated by experts. Following this article on a regular basis boosts students’ confidence in solving complex problems in exams effortlessly. Here, we will learn to find the least common multiple of 45 and 50 with a complete explanation.
What is LCM of 45 and 50?
The Least Common Multiple of 45 and 50 is 450.
How to Find LCM of 45 and 50?
We can obtain the LCM of 45 and 50 by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 45 and 50 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 45 and 50 can be denoted as;
45 = 3 × 3 × 5
50 = 2 × 5 × 5
LCM (45, 50) = 2 × 3 × 3 × 5 × 5 = 450
LCM of 45 and 50 Using Division Method
In the division method, we divide the numbers 45 and 50 by their prime factors until we get the result as one in the complete row. The product of these divisors denotes the least common multiple of 45 and 50.
| 2 | 45 | 50 |
| 3 | 45 | 25 |
| 3 | 15 | 25 |
| 5 | 5 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Therefore, LCM (45, 50) = 2 × 3 × 3 × 5 × 5 = 450
LCM of 45 and 50 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the lowest common multiple among them. The below table represents the multiples of 45 and 50.
| Multiples of 45 | Multiples of 50 |
| 45 | 50 |
| 90 | 100 |
| 135 | 150 |
| 180 | 200 |
| 225 | 250 |
| 270 | 300 |
| 315 | 350 |
| 360 | 400 |
| 405 | 450 |
| 450 | 500 |
LCM (45, 50) = 450
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 45 and 50?
Solution: 450 is the smallest number that is divisible by both 45 and 50.
2. The GCD and LCM of the two numbers are 5 and 450. If one number is 50, calculate the other number.
Solution: Let the other number be p
We know that,
GCD × LCM = 50 × p
p = (GCD × LCM) / 50
p = (5 × 450) / 50
p = 45
Hence the other number is 45.
Frequently Asked Questions on LCM of 45 and 50
What is the LCM of 45 and 50?
What are the methods used to find the LCM of 45 and 50?
The following methods are used to find the LCM of 45 and 50:
Prime Factorisation
Division Method
Listing the Multiples
550 is the LCM of 45 and 50. True or False.
Determine the GCF if the LCM of 45 and 50 is 450.
GCF × LCM = 45 × 50
Given
LCM = 450
GCF × 450 = 45 × 50
GCF = 5
Using prime factorisation, find the LCM of 45 and 50.
Here, we write the numbers as the product of prime factors to find the LCM
45 = 3 × 3 × 5
50 = 2 × 5 × 5
LCM (45, 50) = 2 × 3 × 3 × 5 × 5 = 450
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