LCM of 207 and 138 is 414. For a given set of numbers, the LCM is the smallest number that is a multiple of every one of the numbers. The article LCM of Two Numbers designed by expert faculty is the best guide for students, which enables them to obtain better conceptual knowledge. With the help of this article, students can find the LCM of given numbers in an easy manner. Let us learn how to find the least common multiple of 207 and 138 along with examples and FAQs in this article.
What is LCM of 207 and 138?
The Least Common Multiple of 207 and 138 is 414.
How to Find LCM of 207 and 138?
LCM of 207 and 138 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 207 and 138 Using Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Therefore 207 and 138 can be expressed as;
207 = 3 × 3 × 23
138 = 2 × 3 × 23
LCM (207, 138) = 2 × 3 × 3 × 23 = 414
LCM of 207 and 138 Using Division Method
In this method, we divide the numbers 207 and 138 by a common prime number until the remainder is a prime number or one. The product of these divisors depicts the least common multiple of 207 and 138.
| 2 | 207 | 138 |
| 3 | 207 | 69 |
| 3 | 69 | 23 |
| 23 | 23 | 23 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (207, 138) = 2 × 3 × 3 × 23 = 414
LCM of 207 and 138 Using Listing the Multiples
Here, to find the LCM, we list out the multiples of given numbers. The following table displays the multiples of 207 and 138.
| Multiples of 207 | Multiples of 138 |
| 207 | 138 |
| 414 | 276 |
| 621 | 414 |
| 828 | 552 |
| 1035 | 690 |
LCM (207, 138) = 414
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by both 207 and 138?
Solution: 414 is the smallest number that is divisible by both 207 and 138.
Q. 2: The GCD and LCM of the two numbers are 69 and 414. If one number is 138, calculate the other number.
Solution: Let the other number be p
We know that
GCD × LCM = 138 × p
p = (GCD × LCM) / 138
p = (69 × 414) / 138
p = 207
Hence the other number is 207.
Frequently Asked Questions on LCM of 207 and 138
What is the LCM of 207 and 138?
Is the LCM of 207 and 138 the same as the HCF of 207 and 138?
Is 414 the LCM of 207 and 138?
What are the methods used to find the LCM of 207 and 138?
The methods used to find the LCM of 207 and 138 are as follows:
Prime Factorisation
Division Method
Listing the Multiples
What is the GCF if the LCM of 207 and 138 is 414?
GCF × LCM = 207 × 138
Given
LCM = 414
GCF × 414 = 207 × 138
GCF = 69
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