LCM of 28 and 98 is 196. In Maths, LCM stands for least common multiple. It is essential for students to learn the LCM concept thoroughly as it is one of the most vital concepts in Mathematics. The article LCM of Two Numbers is an essential study tool to obtain the LCM concept more effectively. This article is framed by expert faculty to help students in their exam preparation and clear their doubts based on the LCM concept instantly. Here, we will learn how to find the least common multiple of 28 and 98 using prime factorisation, division method and a list of multiples with a complete explanation.
What is LCM of 28 and 98?
The Least Common Multiple of 28 and 98 is 196.
How to Find LCM of 28 and 98?
LCM of 28 and 98 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 28 and 98 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 28 and 98 can be expressed as;
28 = 2 × 2 × 7
98 = 2 × 7 × 7
LCM (28, 98) = 2 × 2 × 7 × 7 = 196
LCM of 28 and 98 Using Division Method
In the division method, to calculate the least common multiple of 28 and 98, we divide the numbers 28 and 98 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 28 and 98.
| 2 | 28 | 98 |
| 2 | 14 | 49 |
| 7 | 7 | 49 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (28, 98) = 2 × 2 × 7 × 7 = 196
LCM of 28 and 98 Using Listing the Multiples
In this method, we list the multiples of given natural numbers to find the lowest common multiple among them. The below table shows the multiples of 28 and 98.
| Multiples of 28 | Multiples of 98 |
| 28 | 98 |
| 56 | 196 |
| 84 | 294 |
| 112 | 392 |
| 140 | 490 |
| 168 | 588 |
| 196 | 686 |
| 224 | 784 |
LCM (28, 98) = 196
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 28 and 98?
Solution: 196 is the smallest number that is divisible by both 28 and 98.
2. The GCD and LCM of the two numbers are 14 and 196. If one number is 28, what is the other number?
Solution: Let the other number be p
We know that
GCD × LCM = 28 × p
p = (GCD × LCM) / 28
p = (14 × 196) / 28
p = 98
Therefore the other number is 98.
Frequently Asked Questions on LCM of 28 and 98
What is the LCM of 28 and 98?
Is the LCM of 28 and 98 the same as the HCF of 28 and 98?
176 is the LCM of 28 and 98. True or False.
List the methods to find the LCM of 28 and 98.
The methods used to find the LCM of 28 and 98 are
Prime Factorisation
Division Method
Listing the Multiples
What is the GCF if the LCM of 28 and 98 is 196?
GCF × LCM = 28 × 98
Given
LCM = 196
GCF × 196 = 28 × 98
GCF = 14
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