LCM of 50 and 75 is 150.The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. The smallest number among all common multiples of 50 and 75 is the LCM of 50 and 75. (50, 100, 150, 200, 250, 300, 350, etc.) and (75, 150, 225, 300, etc.) are the first few multiples of 50 and 75, respectively. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 50 and 75?
The answer to this question is 150. The LCM of 50 and 75 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 50 and 75, is the smallest positive integer 150 which is divisible by both 50 and 75 with no remainder.
How to Find LCM of 50 and 75?
LCM of 50 and 75 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 50 and 75 Using Prime Factorisation Method
The prime factorisation of 50 and 75, respectively, is given by:
50 = (2 × 5 × 5) = 21 × 52 and
75 = (3 × 5 × 5) = 31 × 52
LCM (50, 75) = 150
LCM of 50 and 75 Using Division Method
We’ll divide the numbers (50, 75) by their prime factors to get the LCM of 50 and 75 using the division method (preferably common). The LCM of 50 and 75 is calculated by multiplying these divisors.
| 5 | 50 | 75 |
| 5 | 10 | 15 |
| 2 | 2 | 3 |
| 3 | 1 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (50, 75) = 150
LCM of 50 and 75 Using Listing the Multiples
To calculate the LCM of 50 and 75 by listing out the common multiples, list the multiples as shown below
| Multiples of 50 | Multiples of 75 |
| 50 | 75 |
| 100 | 150 |
| 150 | 225 |
| 200 | 300 |
| 250 | 375 |
The smallest common multiple of 50 and 75 is 72.
Therefore LCM (50, 75) = 150
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LCM of 50 and 75 Solved Example
Question: The product of two numbers is 3750. If their GCD is 25, what is their LCM?
Solution:
Given: GCD = 25
product of numbers = 3750
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 3750/25
Therefore, the LCM is 150.
The probable combination for the given case is LCM(50, 75) = 150.
Frequently Asked Questions on LCM of 50 and 75
What is the LCM of 50 and 75?
List the methods used to find the LCM of 50 and 75.
What is the Relation Between GCF and LCM of 50, 75?
If the LCM of 75 and 50 is 150, Find its GCF.
Since the LCM of 75 and 50 = 150
⇒ 150 × GCF(75, 50) = 3750
Therefore, the GCF (greatest common factor) = 3750/150 = 25.
How to Find the LCM of 50 and 75 by Prime Factorization?
⇒ LCM of 50, 75 = 2 × 3 × 5 × 5 = 150.
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