LCM of 28 and 42 is 84. LCM denotes the least common factor or multiple of any two or more given integers. LCM of Two Numbers is the best guide students can rely on for effective learning of the LCM concept. Experts prepared this article with the aim to build a stronghold on the concept and score good marks in exams. Solving the problems referring to this article undoubtedly enhances problem-solving abilities and helps them to tackle any type of question in the exams. Let us learn how to find the least common multiple of 28 and 42 with simple steps in this article.
What is LCM of 28 and 42?
The Least Common Multiple of 28 and 42 is 84.
How to Find LCM of 28 and 42?
LCM of 28 and 42 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 28 and 42 Using Prime Factorisation Method
In this method, we can express the numbers 28 and 42 as the product of prime numbers. The numbers 28 and 42 can be expressed as shown below
28 = 2 × 2 × 7
42 = 2 × 3 × 7
LCM (28, 42) = 2 × 2 × 3 × 7 = 84
LCM of 28 and 42 Using Division Method
In this method, to calculate the least common multiple of 28 and 42, we divide the numbers 28 and 42 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 28 and 42.
| 2 | 28 | 42 |
| 2 | 14 | 21 |
| 3 | 7 | 21 |
| 7 | 7 | 7 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (28, 42) = 2 × 2 × 3 × 7 = 84
LCM of 28 and 42 Using Listing the Multiples
In this method, we list out the multiples of 28 and 42 to find their least common multiple. The table mentioned below gives the multiples of 28 and 42.
| Multiples of 28 | Multiples of 42 |
| 28 | 42 |
| 56 | 84 |
| 84 | 126 |
| 112 | 168 |
| 140 | 210 |
| 168 | 252 |
LCM (28, 42) = 84
Related Articles
Prime Factorization 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 28 and 42?
Solution: 84 is the smallest number that is divisible by both 28 and 42.
Q. 2: The product of two numbers is 1176. If their GCD is 14, calculate their LCM.
Solution: Given,
GCD = 14
Product of two numbers = 1176
LCM × GCD = product of two numbers
LCM = Product of two numbers/GCD
LCM = 1176 / 14
LCM = 84
Therefore the least common multiple is 84.
Frequently Asked Questions on LCM of 28 and 42
What is the LCM of 28 and 42?
Is the LCM of 28 and 42 the same as the HCF of 28 and 42?
18 is the HCF of 28 and 42. True or False.
What is the GCF if the LCM of 28 and 42 is 84?
GCF × LCM = 28 × 42
Given
LCM = 84
GCF × 84 = 28 × 42
GCF = 14
Express the relation between GCF and LCM of 28 and 42.
The relation between GCF and LCM of 28 and 42 is
GCF × LCM = 28 × 42
GCF × LCM = 1176
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