LCM of 12 and 14 is 84. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. LCM of 12 and 14 is the smallest number among all common multiples of 12 and 14. The first few multiples of 12 and 14 are (12, 24, 36, 48, 60, 72, 84, . . . ) and (14, 28, 42, 56, 70, 84, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 14 – by listing multiples, by division method, and by prime factorization..
What is LCM of 12 and 14?
The answer to this question is 84. The LCM of 12 and 14 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12 and 14, is the smallest positive integer 84 which is divisible by both 12 and 14 with no remainder.
Also read: Least common multiple
How to Find LCM of 12 and 14?
LCM of 12 and 14 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 14 Using Prime Factorisation Method
The prime factorisation of 12 and 14, respectively, is given by:
12 = (2 × 2 × 3) = 22 × 31 and
14 = (2 × 7) = 21 × 71
LCM (12, 14) = 84
LCM of 12 and 14 Using Division Method
We’ll divide the numbers (12, 14) by their prime factors to get the LCM of 12 and 14 using the division method (preferably common). The LCM of 12 and 14 is calculated by multiplying these divisors.
| 2 | 12 | 14 |
| 2 | 6 | 7 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (12, 14) = 84
LCM of 12 and 14 Using Listing the Multiples
To calculate the LCM of 12 and 14 by listing out the common multiples, list the multiples as shown below
| Multiples of 12 | Multiples of 14 |
| 12 | 14 |
| 24 | 28 |
| 36 | 42 |
| 48 | 56 |
| 60 | 70 |
| 72 | 84 |
| 84 | – |
The smallest common multiple of 12 and 14 is 84.
LCM (12, 14) = 84
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LCM of 12 and 14 Solved Example
Question. The product of two numbers is 168. If their GCD is 2, what is their LCM?
Solution: Given: GCD = 2
product of numbers = 168
LCM × GCD = product of numbers
LCM = Product/GCD = 168/2
Therefore, the LCM is 84.
The probable combination for the given case is LCM(12, 14) = 84.
Frequently Asked Questions on LCM of 12 and 14
What is the LCM of 12 and 14?
List the methods used to find the LCM of 12 and 14.
If the LCM of 14 and 12 is 84, Find its GCF.
Since the LCM of 14 and 12 = 84
⇒ 84 × GCF(14, 12) = 168
Therefore, the greatest common factor (GCF) = 168/84 = 2.
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