LCM of 10 and 50 is 50. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. LCM of 10 and 50 is the smallest number among all common multiples of 10 and 50. The first few multiples of 10 and 50 are (10, 20, 30, 40, 50, 60, . . . ) and (50, 100, 150, 200, . . . ) 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 10 and 50?
The answer to this question is 50. The LCM of 10 and 50 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 10 and 50, is the smallest positive integer 50 which is divisible by both 10 and 50 with no remainder.
How to Find LCM of 10 and 50?
LCM of 10 and 50 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10 and 50 Using Prime Factorisation Method
The prime factorisation of 10 and 50, respectively, is given by:
10 = (2 × 5) = 21 × 51 and
50 = (2 × 5 × 5) = 21 × 52
LCM (10, 50) = 50
LCM of 10 and 50 Using Division Method
We’ll divide the numbers (10, 50) by their prime factors to get the LCM of 10 and 50 using the division method (preferably common). The LCM of 10 and 50 is calculated by multiplying these divisors.
| 2 | 10 | 50 |
| 5 | 5 | 25 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (10, 50) = 50
LCM of 10 and 50 Using Listing the Multiples
To calculate the LCM of 10 and 50 by listing out the common multiples, list the multiples as shown below
| Multiples of 10 | Multiples of 50 |
| 10 | 50 |
| 20 | 100 |
| 30 | 150 |
| 40 | 200 |
| 50 | 250 |
The smallest common multiple of 10 and 50 is 72.
Therefore LCM (24, 36) = 72
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Video Lesson on Applications of LCM
LCM of 10 and 50 Solved Example
Question: The product of two numbers is 500. If their GCD is 10, what is their LCM?
Solution:
Given: GCD = 10
product of numbers = 500
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 500/10
Therefore, the LCM is 50.
The probable combination for the given case is LCM(10, 50) = 50.
Frequently Asked Questions on LCM of 10 and 50
What is the LCM of 10 and 50?
List the methods used to find the LCM of 10 and 50.
If the LCM of 50 and 10 is 50, Find its GCF.
Since the LCM of 50 and 10 = 50
⇒ 50 × GCF(50, 10) = 500
Therefore, the greatest common factor (GCF) = 500/50 = 10.
What is the Relation Between GCF and LCM of 10, 50?
How to Find the LCM of 10 and 50 by Prime Factorization?
LCM of 10, 50 = 50.
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