LCM of 72 and 96 is 288. The least common multiple is the method to determine the smallest possible multiple of two or more numbers. Experts framed the article HCF and LCM in a simple language to help students in effective learning of concepts. Referring to this article while solving the problems clears the doubts of students instantly. Let us learn in detail how to find the least common multiple of 72 and 96 with a complete explanation in this article.
What is LCM of 72 and 96?
The Least Common Multiple of 72 and 96 is 288.
How to Find LCM of 72 and 96?
We can find the LCM of 72 and 96 by using the methods given below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 72 and 96 Using Prime Factorisation Method
By prime factorisation method, the LCM of 72 and 96 can be obtained by multiplying prime factors raised to their respective highest power.
72 = 2 × 2 × 2 × 3 × 3
96 = 2 × 2 × 2 × 2 × 2 × 3
LCM (72, 96) = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288
LCM of 72 and 96 Using Division Method
In the division method, we divide the numbers 45 and 86 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 72 and 96.
| 2 | 72 | 96 |
| 2 | 36 | 48 |
| 2 | 18 | 24 |
| 2 | 9 | 12 |
| 2 | 9 | 6 |
| 3 | 9 | 3 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (72, 96) = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288
LCM of 72 and 96 Using Listing the Multiples
Here, we list out the multiples of 72 and 96 to find the least common multiple of 72 and 96. Let us glance at the multiples of 72 and 96 from the table given below.
| Multiples of 72 | Multiples of 96 |
| 72 | 96 |
| 144 | 192 |
| 216 | 288 |
| 288 | 384 |
| 360 | 480 |
LCM (72, 96) = 288
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Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: The GCD and LCM of the two numbers are 24 and 288. If one number is 96, calculate the other number.
Solution: Let the other number be p.
We know that,
GCD × LCM = 96 × p
p = (GCD × LCM) / 96
p = (24 × 288) / 96
p = 72
Hence the other number is 72.
Q. 2: Find the LCM of 72 and 96 using the prime factorisation method.
Solution: The LCM of 72 and 96 using the prime factorisation method can be determined as below:
72 = 2 × 2 × 2 × 3 × 3
96 = 2 × 2 × 2 × 2 × 2 × 3
LCM (72, 96) = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288
Therefore the least common multiple of 72 and 96 by prime factorisation is 288.
Frequently Asked Questions on LCM of 72 and 96
What is the LCM of 72 and 96?
Is the LCM of 72 and 96 the same as the HCF of 72 and 96?
388 is the LCM of 72 and 96. True or False.
Find the GCF if the LCM of 72 and 96 is 288.
GCF × LCM = 72 × 96
Given
LCM = 288
GCF × 288 = 72 × 96
GCF = 24
Hence the GCF is 24
List the methods used to determine the LCM of 72 and 96.
The methods used to determine the LCM of 72 and 96 are
Prime Factorisation
Division Method
Listing the Multiples
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