LCM of 16, 24 and 40 is 240. The number evenly divisible by 16, 24 and 40 gives you the LCM value. Least common multiples of 16, 24 and 40 are found by listing down the common multiples. (16, 32, 48, 64, 80, ….), (24, 48, 72, 96, 120, ….) and (40, 80, 120, 160, 200,….) are the multiples of 16, 24 and 40. The LCM of two numbers according to prime factorization, division and by listing the multiples methods are explained in a simple to understand manner to help students attain remarkable results in the final exams.
Also read: Least common multiple
What is LCM of 16, 24 and 40?
The answer to this question is 240. The LCM of 16, 24 and 40 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 16, 24 and 40, is the smallest positive integer 240 which is divisible by both 16, 24 and 40 with no remainder.
How to Find LCM of 16, 24 and 40?
LCM of 16, 24 and 40 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 16, 24 and 40 Using Prime Factorisation Method
The prime factorisation of 16, 24 and 40, respectively, is given by:
16 = 2 × 2 × 2 × 2 = 2⁴
24 = 2 × 2 × 2 × 3 = 2³ × 3¹
40 = 2 × 2 × 2 × 5 = 2³× 5¹
LCM (16, 24, 40) = 240
LCM of 16, 24 and 40 Using Division Method
We’ll divide the numbers (16, 24, 40) by their prime factors to get the LCM of 16, 24 and 40 using the division method (preferably common). The LCM of 16, 24 and 40 is calculated by multiplying these divisors.
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2 |
16 |
24 |
40 |
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2 |
8 |
12 |
20 |
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2 |
4 |
6 |
10 |
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2 |
2 |
3 |
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 (16, 24, 40) = 240
LCM of 16, 24 and 40 Using Listing the Multiples
To calculate the LCM of 16, 24 and 40 by listing out the common multiples, list the multiples as shown below
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, . . . .
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, . . . .
Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, . . . .
LCM (16, 24, 40) = 240
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 16, 24 and 40 Solved Examples
Question: In 100, 150, 240 and 60, what is the LCM of 16, 24 and 40?
Solution:
The LCM value is the smallest common multiple which is divisible by 16, 24 and 40 exactly.
The number 240 satisfies this condition.
Hence, the LCM of 16, 24 and 40 is 240.
Frequently Asked Questions on LCM of 16, 24 and 40
What is the LCM of 16, 24 and 40 using the prime factorization method?
To find the LCM using the prime factorization, we should know the prime factors.
16 = 2 × 2 × 2 × 2
24 = 2 × 2 × 2 × 3
40 = 2 × 2 × 2 × 5
LCM of 16, 24 and 40 is the product of prime factors raised to the highest exponent among the numbers 16, 24 and 40
LCM of 16, 24 and 40 = 240
If the LCM of 16, 24 and 40 is 240, find the GCF.
LCM × GCF = 16 × 24 × 40
Given
LCM of 16, 24 and 40 = 240
240 × GCF = 15360
GCF = 15360/240 = 64
Show the relation between GCF and LCM of 16, 24 and 40.
The relation between GCF and LCM of 16, 24 and 40 is
LCM × GCF = 16 × 24 × 40
LCM × GCF = 15360
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