LCM of 207 and 138

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.

lcm of 207 and 138

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

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Prime Factorisation and Division Method for LCM and HCF

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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

Q1

What is the LCM of 207 and 138?

The LCM of 207 and 138 is 414.
Q2

Is the LCM of 207 and 138 the same as the HCF of 207 and 138?

No. The LCM of 207 and 138 is 414 and the HCF of 207 and 138 is 69.
Q3

Is 414 the LCM of 207 and 138?

Yes. The LCM of 207 and 138 is 414.
Q4

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

Q5

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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