LCM of 12 and 32 is 96. The least common multiple of two or more numbers is the smallest number which can be exactly divided by each of the given numbers. Students can make use of the article HCF and LCM on a regular basis to grasp the technique fo representing the least common multiple and highest common factor of given numbers more effectively. Let us learn the simple method of finding the least common multiple of 12 and 32 with the help of the examples and FAQs in this article.
What is LCM of 12 and 32?
The answer to this question is 96.
How to Find LCM of 12 and 32?
LCM of 12 and 32 can be obtained using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 32 Using Prime Factorisation Method
In this method, the LCM of two or more numbers is the product of prime factors. Therefore the numbers 12 and 32 are expressed as;
12 = 2 × 2 × 3
32 = 2 × 2 × 2 × 2 × 2
LCM (12, 32) = 2 × 2 × 2 × 2 × 2 × 3 = 96
LCM of 12 and 32 Using Division Method
In this method, to find the LCM, we divide the numbers 12 and 32 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 12 and 32.
| 2 | 12 | 32 |
| 2 | 6 | 16 |
| 2 | 3 | 8 |
| 2 | 3 | 4 |
| 2 | 3 | 2 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No more further division can be done.
Therefore, LCM (12, 32) = 2 × 2 × 2 × 2 × 2 × 3 = 96
LCM of 12 and 32 Using Listing the Multiples
In this method, we list down the multiples of given numbers to find the lowest common multiple among them. The following table shows the multiples of 12 and 32.
| Multiples of 12 | Multiples of 32 |
| 12 | 32 |
| 24 | 64 |
| 36 | 96 |
| 48 | 128 |
| 60 | 160 |
| 72 | 192 |
| 84 | 224 |
| 96 | 256 |
| 108 | 288 |
LCM (12, 32) = 96
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by both 12 and 32?
Solution: 96 is the smallest number that is divisible by both 12 and 32.
Q. 2: What is the highest common factor of 12 and 32?
Solution: The highest common factor of 12 and 32 is 4.
Frequently Asked Questions on LCM of 12 and 32
What is the LCM of 12 and 32?
Is the LCM of 12 and 32 the same as the HCF of 12 and 32?
Is 86 the LCM of 12 and 32?
Name the methods used to determine the LCM of 12 and 32.
The methods used to determine the LCM of 12 and 32 are:
Prime Factorisation
Division Method
Listing the Multiples
If the LCM of 12 and 32 is 96. What is its GCF?
GCF × LCM = 12 × 32
Given
LCM = 96
GCF × LCM = 12 × 32
GCF = 4
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