LCM of 50 and 80 is 400. The least common multiple denotes the smallest positive integer, which is multiple in a given set of numbers. Professional teachers prepared the article Least Common Multiple (LCM) after acquiring in-depth knowledge of the LCM concept. The main intention to develop such a resource for students is to help them solve problems of higher difficulty levels with ease. In this article, we will learn how to verify th least common multiple of 50 and 80 using a simple method.
What is LCM of 50 and 80?
The Least Common Multiple of 50 and 80 is 400.
How to Find LCM of 50 and 80?
The LCM of 50 and 80 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 50 and 80 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 50 and 80 can be expressed as;
50 = 2 × 5 × 5
80 = 2 × 2 × 2 × 2 × 5
LCM (50, 80) = 2 × 2 × 2 × 2 × 5 × 5 = 400
LCM of 50 and 80 Using Division Method
In the division method, we divide the numbers 50 and 80 by a common prime number until the remainder is a prime number or one. The product of these divisors depicts the least common multiple of 50 and 80.
| 2 | 50 | 80 |
| 2 | 25 | 40 |
| 2 | 25 | 20 |
| 2 | 25 | 10 |
| 5 | 25 | 5 |
| 5 | 5 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (50, 80) = 2 × 2 × 2 × 2 × 5 × 5 = 400
LCM of 50 and 80 Using Listing the Multiples
Here, we list down the multiples of each number until the first common multiple is found among them. The below table shows the multiples of 50 and 80.
| Multiples of 50 | Multiples of 80 |
| 50 | 80 |
| 100 | 160 |
| 150 | 240 |
| 200 | 320 |
| 250 | 400 |
| 300 | 480 |
| 350 | 560 |
| 400 | 640 |
LCM (50, 80) = 400
Related Articles
- Prime Factorisation and Division Method for LCM and HCF
- LCM Calculator
- HCF and LCM
- LCM with Examples
- LCM of Two Numbers
- LCM Formula
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 50 and 80?
Solution: 400 is the smallest number that is divisible by both 50 and 80.
2. The GCD and LCM of two numbers are 10 and 400. If one number is 80, what is the other number?
Solution: Let the other number be m
We know that,
GCD × LCM = 80 × m
m = (GCD × LCM) / 80
m = (10 × 400) / 80
m = 50
Hence the other number is 50.
Frequently Asked Questions on LCM of 50 and 80
What is the LCM of 50 and 80?
Is the LCM of 50 and 80 same as the HCF of 50 and 80?
What are the methods used to find the LCM of 50 and 80?
The following methods are used to find the LCM of 50 and 80
Prime Factorisation
Division method
Listing of Multiples
What is the GCF if the LCM of 50 and 80 is 400?
GCF × LCM = 50 × 80
Given
LCM = 400
GCF × 400 = 50 × 80
GCF = 10
450 is the LCM of 50 and 80. True or False.
False. The LCM of 50 and 80 is 400
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