LCM of 40 and 100 is 200. The smallest number among all common multiples of 40 and 100 is the LCM of 40 and 100. (40, 80, 120, 160, 200, 240, 280, etc.) and (100, 200, 300, 400, 500, etc.) are the first few multiples of 40 and 100, respectively. To find the LCM of 40 and 100, there are three main methods: prime factorization, division, and listing multiples. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers.
Also read: Least common multiple
What is LCM of 40 and 100?
The answer to this question is 200. The LCM of 40 and 100 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 40 and 100, is the smallest positive integer 200 which is divisible by both 40 and 100 with no remainder.
How to Find LCM of 40 and 100?
LCM of 40 and 100 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 40 and 100 Using Prime Factorisation Method
The prime factorisation of 40 and 100, respectively, is given by:
40 = (2 × 2 × 2 × 5) = 23 × 51 and
100 = (2 × 2 × 5 × 5) = 22 × 52
LCM (40, 100) = 200
LCM of 40 and 100 Using Division Method
We’ll divide the numbers (40, 100) by their prime factors to get the LCM of 40 and 100 using the division method (preferably common). The LCM of 40 and 100 is calculated by multiplying these divisors.
| 2 | 40 | 100 |
| 2 | 20 | 50 |
| 2 | 10 | 25 |
| 5 | 5 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (40, 100) = 200
LCM of 40 and 100 Using Listing the Multiples
To calculate the LCM of 40 and 100 by listing out the common multiples, list the multiples as shown below.
| Multiples of 40 | Multiples of 100 |
| 40 | 100 |
| 80 | 200 |
| 120 | 300 |
| 160 | 400 |
| 200 | 500 |
The smallest common multiple of 40 and 100 is 200.
Therefore LCM (40, 100) = 200
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Video Lesson on Applications of LCM
LCM of 40 and 100 Solved Example
Find the smallest number that is divisible by 40 and 100 exactly.
Solution:
The smallest number that is divisible by 40 and 100 exactly is their LCM.
⇒ Multiples of 40 and 100:
Multiples of 40 = 40, 80, 120, 160, 200, 240, . . . .
Multiples of 100 = 100, 200, 300, 400, 500, 600, . . . .
Therefore, the LCM of 40 and 100 is 200.
Frequently Asked Questions on LCM of 40 and 100
What is the LCM of 40 and 100?
List the methods used to find the LCM of 40 and 100.
Which of the following is the LCM of 40 and 100? 28, 18, 200, 36
What is the Relation Between GCF and LCM of 40, 100?
If the LCM of 100 and 40 is 200, Find its GCF.
Since the LCM of 100 and 40 = 200
⇒ 200 × GCF(100, 40) = 4000
Therefore, the greatest common factor (GCF) = 4000/200 = 20.
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