LCM of 30 and 50 is 150. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. LCM of 30 and 50 is the smallest number among all common multiples of 30 and 50. The first few multiples of 30 and 50 are (30, 60, 90, 120, . . . ) and (50, 100, 150, 200, . . . ) respectively.
Also read: Least common multiple
What is LCM of 30 and 50?
The answer to this question is 150. The LCM of 30 and 50 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 30 and 50, is the smallest positive integer 150 which is divisible by both 30 and 50 with no remainder.
How to Find LCM of 30 and 50?
LCM of 30 and 50 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 30 and 50 Using Prime Factorisation Method
The prime factorisation of 30 and 50, respectively, is given by:
30 = (2 × 3 × 5) = 21 × 31 × 51 and
50 = (2 × 5 × 5) = 21 × 52
LCM (30, 50) = 150
LCM of 30 and 50 Using Division Method
We’ll divide the numbers (30, 50) by their prime factors to get the LCM of 30 and 50 using the division method (preferably common). The LCM of 30 and 50 is calculated by multiplying these divisors.
| 2 | 30 | 50 |
| 5 | 15 | 25 |
| 5 | 3 | 5 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (30, 50) = 150
LCM of 30 and 50 Using Listing the Multiples
To calculate the LCM of 30 and 50 by listing out the common multiples, list the multiples as shown below
| Multiples of 30 | Multiples of 50 |
| 30 | 50 |
| 60 | 100 |
| 90 | 150 |
| 120 | 200 |
| 150 | 250 |
The smallest common multiple of 30 and 50 is 150.
Therefore LCM (30, 50) = 150
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Video Lesson on Applications of LCM
LCM of 30 and 50 Solved Examples
The GCD and LCM of two numbers are 10 and 150 respectively. If one number is 30, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 30 × p
⇒ p = (GCD × LCM)/30
⇒ p = (10 × 150)/30
⇒ p = 50
Therefore, the other number is 50.
Frequently Asked Questions on LCM of 30 and 50
What is the LCM of 30 and 50?
List the methods used to find the LCM of 30 and 50.
If the LCM of 50 and 30 is 150, Find its GCF.
Since the LCM of 50 and 30 = 150
⇒ 150 × GCF(50, 30) = 1500
Therefore, the GCF (greatest common factor) = 1500/150 = 10.
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