Solved Examples on Least Common Multiple (LCM)
Example 1: Find the LCM of 8, 12, and 30 by the Prime Factorization Method.
Solution:
- Prime Factors of 8 = 2 × 2 × 2 = 23
- Prime Factors of 12 = 2 × 2 × 3 = 22 × 3
- Prime Factors of 30 = 2 × 3 × 3 × 5 = 2 × 32 × 5
LCM of 8, 12, and 30 = 23× 32 × 5 = 360
Example 2: Find the LCM of 6, 8, and 16.
Solution:
List the multiple of 6, 8, and 16
- Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, …
- Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, …
- Multiple of 16 = 16, 32, 48, 64, ….
The least common multiple of 6, 8, and 16 is 48
Thus, the LCM of 6, 8, and 16 is 48.
Example 3: Find the LCM of 30 and 12 if its HCF is 6.
Solution:
As, 30×12 = 360, and
HCF of 30, 12 = 6
Thus, LCM of 12, 30 = (12×30)/HCF of 12, 30
⇒ LCM of 12, 30 = 360/6
⇒ LCM of 12, 30 = 60
Thus, the LCM of 12 and 30 is 30.
Lowest Common Multiple – LCM
Least Common Multiple in maths is abbreviated as LCM and is used to find a number that is the smallest number that is divisible by two or more numbers perfectly. In other words, the LCM is the smallest multiple that each of the given numbers divides into evenly. LCM stands for Least Common Multiple i.e., LCM is the smallest multiple which is common for all the given numbers. We can easily find the LCM of two or more numbers by simply finding the prime factor of the given numbers and then taking the highest power of each factor of the numbers.
In this article, we will learn about Least Common Multiple (LCM) in maths, how to calculate LCM, its examples, and others in detail.
Table of Content
- What is Least Common Multiple (LCM)?
- How to Find the LCM of two Numbers?
- Finding LCM using Listing Method
- Finding LCM using Prime Factorization Method
- Finding LCM using Division Method
- Least Common Multiple (LCM) Formula
- Relationship Between LCM and HCF
- Difference Between LCM and HCF
- LCM of Three Numbers
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