LCM of 75 and 100 is 300. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The smallest number among all common multiples of 75 and 100 is the LCM of 75 and 100. (75, 150, 225, 300, 375, etc.) and (100, 200, 300, 400, 500, 600, 700, …….) are the first few multiples of 75 and 100, respectively. To find the LCM of 75 and 100, there are three main methods: prime factorization, listing multiples, and division.
Also read: Least common multiple
What is LCM of 75 and 100?
The answer to this question is 300. The LCM of 75 and 100 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 75 and 100, is the smallest positive integer 300 which is divisible by both 75 and 100 with no remainder.
How to Find LCM of 75 and 100?
LCM of 75 and 100 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 75 and 100 Using Prime Factorisation Method
The prime factorisation of 75 and 100, respectively, is given by:
75 = (3 × 5 × 5) = 31 × 52 and
100 = (2 × 2 × 5 × 5) = 22 × 52
LCM (75, 100) = 300
LCM of 75 and 100 Using Division Method
We’ll divide the numbers (75, 100) by their prime factors to get the LCM of 75 and 100 using the division method (preferably common). The LCM of 75 and 100 is calculated by multiplying these divisors.
| 2 | 75 | 100 |
| 2 | 75 | 50 |
| 3 | 75 | 25 |
| 5 | 25 | 25 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (75, 100) = 300
LCM of 75 and 100 Using Listing the Multiples
To calculate the LCM of 75 and 100 by listing out the common multiples, list the multiples as shown below
| Multiples of 75 | Multiples of 100 |
| 75 | 100 |
| 150 | 200 |
| 225 | 300 |
| 300 | 400 |
| 375 | 500 |
The smallest common multiple of 75 and 100 is 300.
Therefore LCM (75, 100) = 300
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Video Lesson on Applications of LCM
LCM of 75 and 100 Solved Example
Question: The product of two numbers is 7500. If their GCD is 25, what is their LCM?
Solution:
Given: GCD = 25
product of numbers = 7500
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 7500/25
Therefore, the LCM is 300.
The probable combination for the given case is LCM(75, 100) = 300.
Frequently Asked Questions on LCM of 75 and 100
What is the LCM of 75 and 100?
List the methods used to find the LCM of 75 and 100.
What is the Relation Between GCF and LCM of 75, 100?
If the LCM of 100 and 75 is 300, Find its GCF.
Since the LCM of 100 and 75 = 300
⇒ 300 × GCF(100, 75) = 7500
Therefore, the GCF (greatest common factor) = 7500/300 = 25.
What is the Least Perfect Square Divisible by 75 and 100?
LCM of 75 and 100 = 2 × 2 × 3 × 5 × 5 [Incomplete pair(s): 3] ⇒ Least perfect square divisible by each 75 and 100 = LCM(75, 100) × 3 = 900 [Square root of 900 = √900 = ±30] Therefore, 900 is the required number.
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