LCM of 12 and 28 is 84. LCM of 12 and 28 is the smallest number among all common multiples of 12 and 28. The first few multiples of 12 and 28 are (12, 24, 36, 48, 60, 72, . . . ) and (28, 56, 84, 112, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 28 – by division method, by listing multiples, and by prime factorization. The LCM of Two Numbers in mathematics is the value that is evenly divisible by the two values.
Also read: Least common multiple
What is LCM of 12 and 28?
The answer to this question is 84. The LCM of 12 and 28 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12 and 28, is the smallest positive integer 84 which is divisible by both 12 and 28 with no remainder.
How to Find LCM of 12 and 28?
LCM of 12 and 28 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 28 Using Prime Factorisation Method
The prime factorisation of 12 and 28, respectively, is given by:
12 = (2 × 2 × 3) = 22 × 31 and
28 = (2 × 2 × 7) = 22 × 71
LCM (12, 28) = 84
LCM of 12 and 28 Using Division Method
We’ll divide the numbers (12, 28) by their prime factors to get the LCM of 12 and 28 using the division method (preferably common). The LCM of 12 and 28 is calculated by multiplying these divisors.
| 2 | 12 | 28 |
| 2 | 6 | 14 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (12, 28) = 84
LCM of 12 and 28 Using Listing the Multiples
To calculate the LCM of 12 and 28 by listing out the common multiples, list the multiples as shown below
| Multiples of 12 | Multiples of 28 |
| 12 | 28 |
| 24 | 56 |
| 36 | 84 |
| 48 | 112 |
| 60 | 140 |
| 72 | 84 |
| 84 | – |
The smallest common multiple of 12 and 28 is 84.
LCM (12, 28) = 84
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LCM of 12 and 28 Solved Example
Question: The product of two numbers is 336. If their GCD is 4, what is their LCM?
Solution:
Given: GCD = 4
product of numbers = 336
LCM × GCD = product of numbers
LCM = Product/GCD = 336/4
Therefore, the LCM is 84.
The probable combination for the given case is LCM(12, 28) = 84.
Frequently Asked Questions on LCM of 12 and 28
What is the LCM of 12 and 28?
List the methods used to find the LCM of 12 and 28.
If the LCM of 28 and 12 is 84, Find its GCF.
Since the LCM of 28 and 12 = 84
⇒ 84 × GCF(28, 12) = 336
Therefore, the greatest common factor (GCF) = 336/84 = 4.
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