LCM of 12, 14 and 16 is 336. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. LCM of 12, 14, and 16 is the smallest number among all common multiples of 12, 14, and 16. The first few multiples of 12, 14, and 16 are (12, 24, 36, 48, 60 . . .), (14, 28, 42, 56, 70 . . .), and (16, 32, 48, 64, 80 . . .) respectively. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 12, 14 and 16?
The answer to this question is 336. The LCM of 12, 14 and 16 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12, 14 and 16, is the smallest positive integer 336 which is divisible by both 12, 14 and 16 with no remainder.
How to Find LCM of 12, 14 and 16?
LCM of 12, 14 and 16 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12, 14 and 16 Using Prime Factorisation Method
The prime factorisation of 12, 14 and 16, respectively, is given by:
12 = (2 × 2 × 3) = 22 × 31,
14 = (2 × 7) = 21 × 71, and
16 = (2 × 2 × 2 × 2) = 24
LCM (12, 14, 16) = 336
LCM of 12, 14 and 16 Using Division Method
We’ll divide the numbers (12, 14, 16) by their prime factors to get the LCM of 12, 14 and 16 using the division method (preferably common). The LCM of 12, 14 and 16 is calculated by multiplying these divisors.
| 2 | 12 | 14 | 16 |
| 2 | 6 | 7 | 8 |
| 2 | 3 | 7 | 4 |
| 2 | 3 | 7 | 2 |
| 3 | 3 | 7 | 1 |
| 7 | 1 | 7 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (12, 14, 16) = 336
LCM of 12, 14 and 16 Using Listing the Multiples
To calculate the LCM of 12, 14 and 16 by listing out the common multiples, list the multiples as shown below
| Multiples of 12 | Multiples of 14 | Multiples of 16 |
| 12 | 14 | 16 |
| 24 | 28 | 32 |
| 36 | 42 | 48 |
| …… | ….. | ……. |
| 336 | 336 | 336 |
The smallest common multiple of 12, 14 and 16 is 72.
Therefore LCM (12, 14, 16) = 336
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LCM of 12, 14 and 16 Solved Example
Find the smallest number that is divisible by 12, 14, 16 exactly.
Solution:
The value of LCM(12, 14, 16) will be the smallest number that is exactly divisible by 12, 14, and 16.
⇒ Multiples of 12, 14, and 16:
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . ., 300, 312, 324, 336, . . . .
Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, . . . ., 280, 294, 308, 322, 336, . . . .
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, . . . ., 304, 320, 336, . . . .
Therefore, the LCM of 12, 14, and 16 is 336.
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