LCM of 7, 14 and 21 is 42. The least common multiple denotes the smallest positive integer which is multiple in a given set of numbers. For a better hold on the LCM concepts, students are advised to refer to the article Least Common Multiple (LCM). The problems based on the LCM concept must be practised thoroughly by the students so that they can solve any type of problem in exams with ease. Here, we will learn how to find the least common multiple of 7, 14 and 21 with the help of solved examples and FAQs.
What is LCM of 7, 14 and 21?
The Least Common Multiple of 7, 14 and 21 is 42.
How to Find LCM of 7, 14 and 21?
The LCM of 7, 14 and 21 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 7, 14 and 21 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 7, 14 and 21 can be expressed as;
7 = 7
14 = 2 × 7
21 = 3 × 7
LCM (7, 14, 21) = 2 × 3 × 7 = 42
LCM of 7, 14 and 21 Using Division Method
In the division method, we divide the numbers 7, 14 and 21 by a common prime number until the remainder is a prime number or one. The product of these divisors shows the least common multiple of 7, 14 and 21.
| 2 | 7 | 14 | 21 |
| 3 | 7 | 7 | 21 |
| 7 | 7 | 7 | 7 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (7, 14, 21) = 2 × 3 × 7 = 42
LCM of 7, 14 and 21 Using Listing the Multiples
Here, we list down the multiples of each number until the first common multiple is found among them. The below table shows the multiples of 7, 14 and 21.
| Multiples of 7 | Multiples of 14 | Multiples of 21 |
| 7 | 14 | 21 |
| 14 | 28 | 42 |
| 21 | 42 | 63 |
| 28 | 56 | 84 |
| 35 | 70 | 105 |
| 42 | 84 | 126 |
LCM (7, 14, 21) = 42
Related Articles
- Prime Factorisation and Division Method for LCM and HCF
- LCM Calculator
- HCF and LCM
- LCM with Examples
- LCM of Two Numbers
- LCM Formula
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 7, 14, 21 exactly?
Solution: We know that the LCM of 7, 14 and 21 will be the smallest number that is divisible by 7, 14, 21 exactly. Here, the LCM of 7, 14 and 21 is 42. Therefore the smallest number that is divisible by 7, 14, 21 exactly is 42.
Frequently Asked Questions on LCM of 7, 14 and 21
What is the LCM of 7, 14 and 21?
Is the LCM of 7, 14 and 21 the same as the HCF of 7 14 and 21?
Is 52 the LCM of 7, 14 and 21?
How to calculate the LCM of 7, 14 and 21 using prime factorisation?
We write the given numbers as the product of prime factors to calculate the LCM
7 = 7
14 = 2 × 7
21 = 3 × 7
LCM (7, 14, 21) = 2 × 3 × 7 = 42
Name the methods used to find the LCM of 7, 14 and 21.
The methods used to find the LCM of 7, 14 and 21 are
Prime Factorisation
Division Method
Listing the Multiples
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