LCM of 14 and 30 is 210. The least common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. Experts developed the article LCM of Two Numbers to provide an easy method of representing the least common multiple of given numbers. Students who master the LCM concepts obtain skills of solving complex problems based on LCM effortlessly. Let us learn how to verify the least common multiple of 14 and 30 with the help of examples in this article.
What is LCM of 14 and 30?
The Least Common Multiple of 14 and 30 is 210.
How to Find LCM of 14 and 30?
We can obtain the LCM of 14 and 30 by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 14 and 30 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 14 and 30 can be expressed as;
14 = 2 × 7
30 = 2 × 3 × 5
LCM (14, 30) = 2 × 3 × 5 × 7 = 210
LCM of 14 and 30 Using Division Method
In the division method, we divide the numbers 14 and 30 by their prime factors until we get the result as one in the complete row. The product of these divisors denotes the least common multiple of 14 and 30.
| 2 | 14 | 30 |
| 3 | 7 | 15 |
| 5 | 7 | 5 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Therefore, LCM (14, 30) = 2 × 3 × 5 × 7 = 210
LCM of 14 and 30 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to calculate the lowest common multiple among them. The multiples of 14 and 30 are as follows:
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ……, 182, 196, 210, ……..
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, ………..
LCM (14, 30) = 210
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 14 and 30?
Solution: 210 is the smallest number that is divisible by both 14 and 30.
2. The GCD and LCM of the two numbers are 2 and 210. If one number is 30, what is the other number?
Solution: Let the other number be z
We know that,
GCD × LCM = 30 × z
z = (GCD × LCM) / 30
z = (2 × 210) / 30
z = 14
Hence the other number is 14.
Frequently Asked Questions on LCM of 14 and 30
What is the LCM of 14 and 30?
What are the methods used to find the LCM of 14 and 30?
The following methods are used to find the LCM of 14 and 30:
Prime Factorisation
Division Method
Listing the Multiples
200 is the LCM of 14 and 30. True or False.
Write the LCM of 14 and 30 and the HCF of 14 and 30.
Mention the relation between GCF and LCM of 14 and 30.
The equation used to represent the relation between GCF and LCM of 14 and 30 is
GCF × LCM = 14 × 30
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