LCM of 2, 3 and 7 is 42. LCM denotes the least common factor or multiple of any two or more given numbers. For a perfect knowledge of the LCM concept, use the article LCM with Examples as reference material anytime and anywhere. Students will also be able to face the exam confidently by going through this article on a regular basis. Here, we will learn how to verify the least common multiple of 2, 3 and 7 in an accurate manner.
What is LCM of 2, 3 and 7?
The Least Common Multiple of 2, 3, and 7 is 42.
How to Find LCM of 2, 3 and 7?
LCM of 2, 3 and 7 can be obtained by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 2, 3 and 7 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 2, 3 and 7 are expressed as;
2 = 2
3 = 3
7 = 7
LCM (2, 3, 7) = 2 × 3 × 7 = 42
LCM of 2, 3 and 7 Using Division Method
In the division method, to find the least common multiple of 2, 3 and 7, we divide the numbers 2, 3 and 7 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 2, 3 and 7.
| 2 | 2 | 3 | 7 |
| 3 | 1 | 3 | 7 |
| 7 | 1 | 1 | 7 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (2, 3, 7) = 2 × 3 × 7 = 42
LCM of 2, 3 and 7 Using Listing the Multiples
In this method, we list down the multiples of given numbers to find the lowest common multiple among them. A few multiples of 2, 3 and 7 are given below.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ……, 38, 40, 42, ………
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ………, 36, 39, 42, ……
Multiples of 7: 7, 14, 21, 28, 35, 42, …………
LCM (2, 3, 7) = 42
Related Articles
- Lowest Common Multiple (LCM)
- Prime Factorisation and Division Method for LCM and HCF
- LCM of Two Numbers
- LCM calculator
- LCM Formula
- HCF and LCM
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 2, 3, 7 exactly?
Solution: The smallest number that is divisible by 2, 3, 7 exactly is their LCM. We know that the LCM of 2, 3 and 7 is 42. Hence the smallest number that is divisible by 2, 3, 7 exactly is 42.
Frequently Asked Questions on LCM of 2, 3 and 7
What is the LCM of 2, 3 and 7?
Mention the LCM of 2, 3 and 7 and the HCF of 2 3 and 7.
Name the methods used to find the LCM of 2, 3 and 7.
The methods used to find the LCM of 2, 3 and 7 are:
Prime Factorisation
Division method
Listing the Multiples
Find the LCM of 2, 3 and 7 using the prime factorisation method.
In prime factorisation, we write the given numbers as the product of prime factors to find the LCM
2 = 2
3 = 3
7 = 7
LCM (2, 3, 7) = 2 × 3 × 7 = 42
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