LCM of 3 and 11 is 33. LCM represents the smallest positive number which is a multiple of two or more numbers. By regularly going through the article Least Common Multiple (LCM), solving the problems based on the LCM concept will become an easy task for the students. High professional teachers designed the article in a simple and precise manner so that students grasp the concept effortlessly and attain a remarkable score in the exams. Let us learn how to calculate the least common multiple of 3 and 11 with a complete explanation here.
What is LCM of 3 and 11?
The answer to this question is 33.
How to Find LCM of 3 and 11?
LCM of 3 and 11 can be determined by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 3 and 11 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence, the numbers 3 and 11 can be expressed as;
3 = 3
11 = 11
LCM (3, 11) = 3 × 11 = 33
LCM of 3 and 11 Using Division Method
In this method, we divide the numbers 3 and 11 by a common prime number until the remainder is a prime number or one. The product of these divisors denotes the least common multiple of 3 and 11.
| 3 | 3 | 11 |
| 11 | 1 | 11 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (3, 11) = 3 × 11 = 33
LCM of 3 and 11 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the lowest common multiple among them. The below table shows the multiples of 3 and 11.
| Multiples of 3 | Multiples of 11 |
| 3 | 11 |
| 6 | 22 |
| 9 | 33 |
| 12 | 44 |
| 15 | 55 |
| 18 | 66 |
| 21 | 77 |
| 24 | 88 |
| 27 | 99 |
| 30 | 110 |
| 33 | 121 |
LCM (3, 11) = 33
Related Articles
- HCF and LCM
- LCM calculator
- LCM of Two Numbers
- Prime Factorization and Division Method for LCM and HCF
- LCM Formula
- LCM with Examples
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 3 and 11?
Solution: 33 is the smallest number that is divisible by both 3 and 11.
2. What is the LCM if the product of two numbers is 33 and their GCD is 1?
Solution: Given
GCD = 1
Product of numbers = 33
We know that
GCF × LCM = Product of numbers
LCM = 33/1
LCM = 33
Hence the LCM is 33.
Frequently Asked Questions on LCM of 3 and 11
What is the LCM of 3 and 11?
Is the LCM of 3 and 11 the same as the HCF of 3 and 11?
How to find the LCM of 3 and 11 by prime factorisation?
In the prime factorisation method, the given numbers are expressed as the product of prime factors
3 = 3
11 = 11
LCM (3, 11) = 3 × 11 = 33
Hence, the LCM of 3 and 11 by prime factorisation is 33.
Mention the methods to determine the LCM of 3 and 11.
The methods used to determine the LCM of 3 and 11 are
Prime Factorisation
Division Method
Listing the Multiples
What is the GCF if the LCM of 3 and 11 is 33?
GCF × LCM = 3 × 11
Given
LCM = 33
GCF × 33 = 3 × 11
GCF = 1
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