LCM of 10 and 30 is 30. LCM of 10 and 30 is the smallest number among all common multiples of 10 and 30. The first few multiples of 10 and 30 are (10, 20, 30, 40, 50, 60, 70, . . . ) and (30, 60, 90, 120, . . . ) respectively. 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.
Also read: Least common multiple
What is LCM of 10 and 30?
The answer to this question is 30. The LCM of 10 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 10 and 30, is the smallest positive integer 30 which is divisible by both 10 and 30 with no remainder.
How to Find LCM of 10 and 30?
LCM of 10 and 30 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10 and 30 Using Prime Factorisation Method
The prime factorisation of 10 and 30, respectively, is given by:
10 = (2 × 5) = 21 × 51
and 30 = (2 × 3 × 5) = 21 × 31 × 51
LCM (10, 30) = 30
LCM of 10 and 30 Using Division Method
We’ll divide the numbers (10, 30) by their prime factors to get the LCM of 10 and 30 using the division method (preferably common). The LCM of 10 and 30 is calculated by multiplying these divisors.
| 2 | 10 | 30 |
| 5 | 5 | 15 |
| 3 | 1 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (10, 30) = 30
LCM of 10 and 30 Using Listing the Multiples
To calculate the LCM of 10 and 30 by listing out the common multiples, list the multiples as shown below:
| Multiples of 10 | Multiples of 30 |
| 10 | 30 |
| 20 | 60 |
| 30 | 90 |
| 40 | 120 |
| 50 | 150 |
The smallest common multiple of 10 and 30 is 30.
Therefore LCM (10, 30) = 30
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LCM of 10 and 30 Solved Examples
Question: The GCD and LCM of two numbers are 10 and 30 respectively. If one number is 10, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 10 × p
⇒ p = (GCD × LCM)/10
⇒ p = (10 × 30)/10
⇒ p = 30
Therefore, the other number is 30.
Frequently Asked Questions on LCM of 10 and 30
What is the LCM of 10 and 30?
Which of the following is the LCM of 10 and 30? 40, 5, 28, 30
If the LCM of 30 and 10 is 30, Find its GCF.
Since the LCM of 30 and 10 = 30
⇒ 30 × GCF(30, 10) = 300
Therefore, the greatest common factor (GCF) = 300/30 = 10.
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