LCM of 120 and 150 is 600. LCM denotes the smallest positive number that is a multiple of two or more numbers. The article LCM with Examples will explain the concept in a comprehensive manner so that students obtain good marks in examinations. This article acts as a tool for students to learn and revise the concepts in a better way. Let us learn how to determine the least common multiple of 120 and 150 with a complete explanation here.
What is LCM of 120 and 150?
The Least Common Multiple of 120 and 150 is 600.
How to Find LCM of 120 and 150?
LCM of 120 and 150 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 120 and 150 Using Prime Factorisation Method
In the prime factorisation method, LCM of 120 and 150 can be obtained by multiplying prime factors raised to their respective highest power.
120 = 2 × 2 × 2 × 3 × 5
150 = 2 × 3 × 5 × 5
LCM (120, 150) = 2 × 2 × 2 × 3 × 5 × 5 = 600
LCM of 120 and 150 Using Division Method
In the division method, to find the LCM, we divide the numbers 120 and 150 by their prime factors until we get the result as one in the complete row. The product of these divisors shows the least common multiple of 120 and 150.
| 2 | 120 | 150 |
| 2 | 60 | 75 |
| 2 | 30 | 75 |
| 3 | 15 | 75 |
| 5 | 5 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (120, 150) = 2 × 2 × 2 × 3 × 5 × 5 = 600
LCM of 120 and 150 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the least common multiple among them. Let us have a look at the multiples of 120 and 150 from the table given below.
| Multiples of 120 | Multiples of 150 |
| 120 | 150 |
| 240 | 300 |
| 360 | 450 |
| 480 | 600 |
| 600 | 750 |
LCM (120, 150) = 600
Related Articles
- Least Common Multiple (LCM)
- HCF and LCM
- LCM Calculator
- LCM of Two Numbers
- LCM Formula
- Prime Factorisation 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 120 and 150?
Solution: 600 is the smallest number that is divisible by both 120 and 150.
2. The GCD and LCM of the two numbers are 30 and 600. If one number is 150, what is the other number?
Solution: Let the other number be z
We know that,
GCD × LCM = 150 × z
z = (GCD × LCM) / 150
z = (30 × 600) / 150
z = 120
Thus the other number is 120.
Frequently Asked Questions on LCM of 120 and 150
What is the LCM of 120 and 150?
Is the LCM of 120 and 150 same as the HCF of 120 and 150?
What are the methods used to find the least common multiple of 120 and 150?
The methods used to find the least common multiple of 120 and 150 are
Prime Factorisation
Division method
Listing the Multiples
What is the GCF if the LCM of 120 and 150 is 600?
GCF × LCM = 120 × 150
Given
LCM = 600
GCF × 600 = 120 × 150
GCF = 30
Using the prime factorisation method, find the LCM of 120 and 150.
Here, we write the numbers as the product of prime factors to find the LCM
120 = 2 × 2 × 2 × 3 × 5
150 = 2 × 3 × 5 × 5
LCM (120, 150) = 2 × 2 × 2 × 3 × 5 × 5 = 600
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