LCM of 32 and 40 is 160. The smallest positive number that is a multiple of two or more numbers is known as Least Common Multiple. LCM with Examples is the best reference guide students can rely on for in-depth knowledge of LCM. This article is designed in a simple and understandable language so that students grasp the concept more easily irrespective of their intelligence quotient. Learn how to find the least common multiple of 32 and 40 using prime factorisation, division method and listing multiples in this article.
What is LCM of 32 and 40?
The Least Common Multiple of 32 and 40 is 160.
How to Find LCM of 32 and 40?
By using the following methods, we can find the LCM of 32 and 40:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 32 and 40 Using Prime Factorisation Method
By prime factorisation method, we can write 32 and 40 as the product of prime numbers, such that;
32 = 2 × 2 × 2 × 2 × 2
40 = 2 × 2 × 2 × 5
LCM (32, 40) = 2 × 2 × 2 × 2 × 2 × 5 = 160
LCM of 32 and 40 Using Division Method
The least common multiple of 32 and 40 can be determined by dividing the numbers 32 and 40 by their prime factors until we get the result as one in the complete row. The product of these divisors illustrates the least common multiple of 32 and 40.
| 2 | 32 | 40 |
| 2 | 16 | 20 |
| 2 | 8 | 10 |
| 2 | 4 | 5 |
| 2 | 2 | 5 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (32, 40) = 2 × 2 × 2 × 2 × 2 × 5 = 160
LCM of 32 and 40 Using Listing the Multiples
In this method, by listing the multiples of 32 and 40, we can find the lowest common multiple of 32 and 40. The multiples of 32 and 40 are shown in the below table.
| Multiples of 32 | Multiples of 40 |
| 32 | 40 |
| 64 | 80 |
| 96 | 120 |
| 128 | 160 |
| 160 | 200 |
| 192 | 240 |
| 224 | 280 |
| 256 | 320 |
LCM (32, 40) = 160
Related Articles
Prime Factorisation and Division Method for HCF and LCM
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by both 32 and 40?
Solution: 160 is the smallest number that is divisible by both 32 and 40.
Q. 2: The GCD and LCM of two numbers are 8 and 160. If one number is 40, what is the other number?
Solution: Let the other number be q
We know that,
GCD × LCM = 40 × q
q = (GCD × LCM)/40
q = (8 × 160)/40
q = 32
Thus the other number is 32.
Frequently Asked Questions on LCM of 32 and 40
What is the LCM of 32 and 40?
Is the LCM of 32 and 40 the same as the HCF of 32 and 40?
How do you find the LCM of 32 and 40 by listing multiples?
First, list the multiples of 32 and 40
Multiples of 32 = 32, 64, 96, 128, 160, 192, 224,…..
Multiples of 40 = 40, 80, 120, 160, 200, 240, 280,….
Here the LCM of 32 and 40 is 160
Therefore the least common multiple of 32 and 40 by listing multiples is 160
Mention the methods used to find the LCM of 32 and 40.
The methods used to find the LCM of 32 and 40 are
Prime Factorisation
Division Method
Listing the Multiples
Comments