LCM of 4, 6 and 7 is 84. In Maths, the full form of LCM is the least common multiple. Teachers of high experience designed the article LCM of Two Numbers in a detailed manner so that students while solving the problems get a thorough knowledge of the LCM concept. This article helps students to learn the technique of determining the least common multiple of given numbers quickly. In this article, we will learn how to find the least common multiple of 4, 6 and 7 using prime factorisation, division method and a list of multiples.
What is LCM of 4, 6 and 7?
The Least Common Multiple of 4, 6 and 7 is 84.
How to Find LCM of 4, 6 and 7?
LCM of 4, 6 and 7 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 4, 6 and 7 Using Prime Factorisation Method
Here, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree. Hence, the numbers 4, 6, and 7 can be expressed as;
4 = 2 × 2
6 = 2 × 3
7 = 7
LCM (4, 6, 7) = 2 × 2 × 3 × 7 = 84
LCM of 4, 6 and 7 Using Division Method
In the division method, to calculate the least common multiple of 4, 6 and 7, we divide the numbers 4, 6 and 7 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 4, 6 and 7.
| 2 | 4 | 6 | 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 (4, 6, 7) = 2 × 2 × 3 × 7 = 84
LCM of 4, 6 and 7 Using Listing the Multiples
In this method, we list the multiples of given natural numbers to find the lowest common multiple among them. The multiples of 4, 6 and 7 are as follows:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …….., 68, 72, 76, 80, 84, ……
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ……, 72, 78, 84, …..
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, …………
LCM (4, 6, 7) = 84
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 4, 6, 7 exactly?
Solution: The smallest number that is divisible by 4, 6, 7 exactly is their LCM. The LCM of 4, 6 and 7 is 84. Hence, the smallest number that is divisible by 4, 6 and 7 is 84.
Frequently Asked Questions on LCM of 4, 6 and 7
What is the LCM of 4, 6 and 7?
Is the LCM of 4, 6 and 7 the same as the HCF of 4, 6, and 7?
Is 94 the LCM of 4, 6 and 7?
Name the methods used to find the LCM of 4, 6 and 7.
The following methods are used to find the LCM of 4, 6 and 7
Prime Factorisation
Division Method
Listing the Multiples
Determine the LCM of 4, 6 and 7 using prime factorisation.
In prime factorisation, the given numbers are expressed as the product of prime factors to calculate the LCM
4 = 2 × 2
6 = 2 × 3
7 = 7
LCM (4, 6, 7) = 2 × 2 × 3 × 7 = 84
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