LCM of 9 and 42 is 126. LCM is defined as the smallest common multiple of two or more numbers. The article LCM of Two Numbers helps students to clear their doubts by offering in-depth knowledge of the LCM concept. This article is designed in a well-structured format to provide the best method of solving the problems with speed and correctness. Let us learn how to find the least common multiple of 9 and 42 using prime factorisation, division method and a list of multiples in detail here.
What is LCM of 9 and 42?
The Least Common Multiple of 9 and 42 is 126.
How to Find LCM of 9 and 42?
LCM of 9 and 42 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 9 and 42 Using Prime Factorisation Method
Here, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree. Hence, the numbers 9 and 42 can be expressed as;
9 = 3 × 3
42 = 2 × 3 × 7
LCM (9, 42) = 2 × 3 × 3 × 7 = 126
LCM of 9 and 42 Using Division Method
In the division method, to calculate the least common multiple of 9 and 42, we divide the numbers 9 and 42 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 9 and 42.
| 2 | 9 | 42 |
| 3 | 9 | 21 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 42) = 2 × 3 × 3 × 7 = 126
LCM of 9 and 42 Using Listing the Multiples
In this method, we list the multiples of given natural numbers to find the lowest common multiple among them. The multiples of 9 and 42 are as follows:
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, …….
Multiples of 42: 42, 84, 126,168, 210, 252, 294, 336, 378, 420,…………
LCM (9, 42) = 126
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 9 and 42?
Solution: 126 is the smallest number that is divisible by both 9 and 42.
2. What is the LCM if the product of two numbers is 378 and their GCD is 3?
Solution: Given
GCD = 3
Product of numbers = 378
We know that
GCD × LCM = Product of numbers
LCM = Product of numbers / GCD
LCM = 378 / 3
LCM = 126
Therefore, the LCM is 126.
Frequently Asked Questions on LCM of 9 and 42
What is the LCM of 9 and 42?
Is the LCM of 9 and 42 the same as the HCF of 9 and 42?
146 is the LCM of 9 and 42. True or False.
Find the GCF if the LCM of 9 and 42 is 126.
GCF × LCM = 9 × 42
Given
LCM = 126
GCF × 126 = 9 × 42
GCF = 3
What are the methods used to find the LCM of 9 and 42?
The below methods are used to find the LCM of 9 and 42
Prime Factorisation
Division Method
Listing the Multiples
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