LCM of 72 and 84 is 504. The LCM is the method to find the least common multiple between any two or more numbers. It is very important to follow the right study guide for a better understanding of the concepts. For this reason, experts have formulated the article Prime Factorisation and Division Method for LCM and HCF in a simple and easy language. Regular use of this article enables students to solve tricky problems based on the LCM and HCF with ease in a short duration. Here, we will discuss how to find the least common multiple of 72 and 84 in a detailed manner.
What is LCM of 72 and 84?
The Least Common Multiple of 72 and 84 is 504.
How to Find LCM of 72 and 84?
LCM of 72 and 84 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 72 and 84 Using Prime Factorisation Method
In the prime factorisation method, LCM of 72 and 84 can be obtained by multiplying prime factors raised to their respective highest power.
72 = 2 × 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
LCM (72, 84) = 2 × 2 × 2 × 3 × 3 × 7 = 504
LCM of 72 and 84 Using Division Method
In the division method, to find the least common multiple of 72 and 84, we divide the numbers 72 and 84 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 72 and 84.
| 2 | 72 | 84 |
| 2 | 36 | 42 |
| 2 | 18 | 21 |
| 3 | 9 | 21 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (72, 84) = 2 × 2 × 2 × 3 × 3 × 7 = 504
LCM of 72 and 84 Using Listing the Multiples
In this method, we list down the multiples of 72 and 84 to find the least common multiple among them. The below table shows the multiples of 72 and 84.
| Multiples of 72 | Multiples of 84 |
| 72 | 84 |
| 144 | 168 |
| 216 | 252 |
| 288 | 336 |
| 360 | 420 |
| 432 | 504 |
| 504 | 588 |
| 576 | 672 |
LCM (72, 84) = 504
Related Articles
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 72 and 84?
Solution: 504 is the smallest number that is divisible by both 72 and 84.
2. The product of the two numbers is 6048. If their GCD is 12, calculate their LCM.
Solution: Given
GCD = 12
Product of numbers = 6048
We know that
GCD × LCM = Product of numbers
LCM = Product of numbers / GCD
LCM = 6048 / 12
LCM = 504
Therefore the LCM is 504.
Frequently Asked Questions on LCM of 72 and 84
What is the LCM of 72 and 84?
Is the LCM of 72 and 84 the same as the HCF of 72 and 84?
Name the methods used to find the LCM of 72 and 84.
The methods used to find the LCM of 72 and 84 are as follows:
Prime Factorisation
Division method
Listing the Multiples
What is the GCF if the LCM of 72 and 84 is 504?
GCF × LCM = 72 × 84
Given
LCM = 504
GCF × 504 = 72 × 84
GCF = 12
Write the relation between the GCF and LCM of 72 and 84.
The equation used to express the relation between GCF and LCM of 72 and 84 is
GCF × LCM = 72 × 84
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