LCM of 3, 4 and 7 is 84. The smallest common multiple which is divisible by given numbers is the LCM value. Least common multiples of 3, 4 and 7 can be determined by knowing the multiples of each number. (3, 6, 9, 12, 15, 18, 21, ….), (4, 8, 12, 16, 20, 24, …..) and (7, 14, 21, 28, 35, 42, ….) are the multiples of 3, 4 and 7. In this article, LCM of two numbers using the listing of multiples, prime factorization and division methods are explained in brief.
Also read: Least common multiple
What is LCM of 3, 4 and 7?
The answer to this question is 84. The LCM of 3, 4 and 7 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3, 4 and 7, is the smallest positive integer 84 which is divisible by both 3, 4 and 7 with no remainder.
How to Find LCM of 3, 4 and 7?
LCM of 3, 4 and 7 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 4 and 7 Using Prime Factorisation Method
The prime factorisation of 3, 4 and 7, respectively, is given by:
3 = 3 = 3¹
4 = 2 × 2 = 2²
7 = 7 = 7¹
LCM (3, 4, 7) = 84
LCM of 3, 4 and 7 Using Division Method
We’ll divide the numbers (3, 4, 7) by their prime factors to get the LCM of 3, 4 and 7 using the division method (preferably common). The LCM of 3, 4 and 7 is calculated by multiplying these divisors.
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2 |
3 |
4 |
7 |
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2 |
3 |
2 |
7 |
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3 |
3 |
1 |
7 |
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7 |
1 |
1 |
7 |
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× |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (3, 4, 7) = 84
LCM of 3, 4 and 7 Using Listing the Multiples
To calculate the LCM of 3, 4 and 7 by listing out the common multiples, list the multiples as shown below
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 75, 78, 81, 84, . . . .
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 76, 80, 84, . . . .
Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, . . . ., 63, 70, 77, 84, . . . .
LCM (3, 4, 7) = 84
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 3, 4 and 7 Solved Examples
Question: Among 84, 34, 22 and 50, what is the LCM of 3, 4 and 7?
Solution:
We know that
LCM value is the smallest number which is divisible exactly by 3, 4 and 7.
The number which satisfies this condition is 84.
Hence, the LCM of 3, 4 and 7 is 84.
Frequently Asked Questions on LCM of 3, 4 and 7
What are the methods used to find the LCM of 3, 4 and 7?
With the help of prime factorisation, find the LCM of 3, 4 and 7.
To find the LCM, the factors must be known
3 = 3 = 3¹
4 = 2 × 2 = 2²
7 = 7 = 7¹
LCM is the product of prime factors raised to the highest exponent among 3, 4 and 7.
LCM of 3, 4 and 7 = 84
What is the LCM of 3, 4 and 7?
Write the relation between GCF and LCM of 3, 4 and 7.
The relation between GCF and LCM of 3, 4 and 7 are
GCF × LCM = 3 × 4 × 7
GCF × LCM = 84
Determine the GCF if the LCM of 3, 4 and 7 is 84.
Given
LCM of 3, 4 and 7 = 84
LCM × GCF = 3 × 4 × 7
84 × GCF = 84
GCF = 84/84 = 1
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