LCM Formula Examples
Example 1: Find out the LCM of 4 and 10.
Solution:
we know that LCM(a, b) = a × b/ GCD(a, b)
Here, a = 4 and b = 10
a × b = 4 × 10 = 40
GCD(a, b) = 2
Hence, LCM(16, 10) = 40 /2 = 20
Example 2: Calculate the LCM of 14, 12, 7, and 8.
Solution:
LCM of 14, 12, 7, 8 = 2 × 2 × 2 × 3 × 7
= 168
Hence, LCM(14, 12, 7, 8) = 168
Example 3: Find out the LCM for 8 and 24.
Solution:
Prime Factorization of 8 = 2 × 2 × 2
Prime Factorization of 24 = 2 × 2 × 2 × 3
LCM = 2 × 2 × 2 × 3= 24
Example 4: Find out the LCM of 36, 24.
Solution:
Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360 etc.
Multiples of 24 = 24, 48, 72, 96, 120, etc.
Common multiple = 72
Hence, LCM of 36 and 24 = 72
Example 5: Find the least number divided by 48 and 72, which leaves the remainder 9 in each.
Solution:
First we find the LCM of the two numbers we get,
Prime Factorisation of 48 = 2 × 2 × 2 × 2 × 3
Prime Factorization of 72 = 2 × 2 × 2 × 3 × 3
Therefore, LCM of the two numbers is 2 × 2 × 2 × 2 × 3 × 3 = 144.
The least number divided by 48 and 76 leaving remainder 9 is (144 + 9) = 153.
LCM Formula
LCM Formula: LCM stands for Least Common Multiple. LCM of two numbers say a and b is defined as the smallest positive integer divisible by both the numbers a and b. Hence, the LCM is the smallest common multiple of two or more numbers. It is also called lowest common multiple, or smallest common multiple.
In this article, we will discuss LCM, Formulas to calculate LCM, and different methods used to find the LCM of two or more numbers.
Table of Content
- What is LCM?
- LCM Formula
- Finding LCM using HCF Formula
- LCM Formula for 2 Numbers
- LCM of Fractions
- LCM Calculator
- How to Find LCM (Lowest Common Multiple)?
- LCM by Listing Multiples
- LCM using Prime Factorization Method
- LCM using Division Method
- LCM Formula Examples
- Practice Questions on LCM Formula
- Properties of LCM
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