LCM of 4, 9 and 10 is 180. The method used to determine the smallest common multiple between the given numbers is the LCM value. Least common multiples of 4, 9 and 10 can be found from the common multiples as shown in this article. (4, 8, 12, 16, 20, 24, ….), (9, 18, 27, 36, 45, …..) and (10, 20, 30, 40, 50, 60, ….) are the multiples of 4, 9 and 10. The LCM of two numbers using the listing of multiples, prime factorization and division methods are discussed here.
Also read: Least common multiple
What is LCM of 4, 9 and 10?
The answer to this question is 180. The LCM of 4, 9 and 10 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 4, 9 and 10, is the smallest positive integer 180 which is divisible by both 4, 9 and 10 with no remainder.
How to Find LCM of 4, 9 and 10?
LCM of 4, 9 and 10 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 4, 9 and 10 Using Prime Factorisation Method
The prime factorisation of 4, 9 and 10, respectively, is given by:
4 = 2 × 2 = 2²
9 = 3 × 3 = 3²
10 = 2 × 5 = 2¹× 5¹
LCM (4, 9, 10) = 180
LCM of 4, 9 and 10 Using Division Method
We’ll divide the numbers (4, 9, 10) by their prime factors to get the LCM of 4, 9 and 10 using the division method (preferably common). The LCM of 4, 9 and 10 is calculated by multiplying these divisors.
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2 |
4 |
9 |
10 |
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2 |
2 |
9 |
5 |
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3 |
1 |
9 |
5 |
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3 |
1 |
3 |
5 |
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5 |
1 |
1 |
5 |
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× |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (4, 9, 10) = 180
LCM of 4, 9 and 10 Using Listing the Multiples
To calculate the LCM of 4, 9 and 10 by listing out the common multiples, list the multiples as shown below
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 164, 168, 172, 176, 180, . . . .
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . ., 153, 162, 171, 180, . . . .
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, . . . ., 160, 170, 180, . . . .
LCM (4, 9, 10) = 180
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 4, 9 and 10 Solved Examples
Question: Among 180, 24, 12 and 40, what is the LCM of 4, 9 and 10?
Solution:
We know that
LCM value is the smallest number which is divisible exactly by 4, 9 and 10.
The number which satisfies this condition is 180.
Hence, the LCM of 4, 9 and 10 is 180.
Frequently Asked Questions on LCM of 4, 9 and 10
What are the methods used to find the LCM of 4, 9 and 10?
With the help of prime factorisation, find the LCM of 4, 9 and 10.
To find the LCM, the factors must be known
4 = 2 × 2
9 = 3 × 3
10 = 2 × 5
LCM is the product of prime factors raised to the highest exponent among 4, 9 and 10.
LCM of 4, 9 and 10 = 180
What is the LCM of 4, 9 and 10?
Write the relation between GCF and LCM of 4, 9 and 10.
The relation between GCF and LCM of 4, 9 and 10 are
GCF × LCM = 4 × 9 × 10
GCF × LCM = 360
Determine the GCF if the LCM of 4, 9 and 10 is 180.
Given
LCM of 4, 9 and 10 = 180
LCM × GCF = 4 × 9 × 10
180 × GCF = 360
GCF = 360/180 = 2
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