LCM of 14 and 15 is 210. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. The smallest number among all common multiples of 14 and 15 is the LCM of 14 and 15. (14, 28, 42, 56, etc.) and (15, 30, 45, 60, 75, 90, 105, etc.) are the first few multiples of 14 and 15. There are three typical ways for calculating the LCM of 14 and 15: prime factorization, listing multiples, and division.
Also read: Least common multiple
What is LCM of 14 and 15?
The answer to this question is 210. The LCM of 14 and 15 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 14 and 15, is the smallest positive integer 210 which is divisible by both 14 and 15 with no remainder.
How to Find LCM of 14 and 15?
LCM of 14 and 15 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 14 and 15 Using Prime Factorisation Method
The prime factorisation of 14 and 15, respectively, is given by:
14 = (2 × 7) = 21 × 71 and
15 = (3 × 5) = 31 × 51
LCM (14, 15) = 210
LCM of 14 and 15 Using Division Method
We’ll divide the numbers (14, 15) by their prime factors to get the LCM of 14 and 15 using the division method (preferably common). The LCM of 14 and 15 is calculated by multiplying these divisors.
| 2 | 14 | 15 |
| 3 | 7 | 15 |
| 5 | 7 | 5 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (14, 15) = 210
LCM of 14 and 15 Using Listing the Multiples
To calculate the LCM of 14 and 15 by listing out the common multiples, list the multiples as shown below
| Multiples of 14 | Multiples of 15 |
| 14 | 15 |
| 28 | 30 |
| 42 | 45 |
| …… | ….. |
| 210 | 210 |
The smallest common multiple of 14 and 15 is 210.
Therefore LCM (14, 15) = 210
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Video Lesson on Applications of LCM
LCM of 14 and 15 Solved Example
Question: Find the smallest number that is divisible by 14 and 15 exactly.
Solution:
The smallest number that is divisible by 14 and 15 exactly is their LCM.
⇒ Multiples of 14 and 15:
Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, . . . .
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, . . . .
Therefore, the LCM of 14 and 15 is 210.
Frequently Asked Questions on LCM of 14 and 15
What is the LCM of 14 and 15?
List the methods used to find the LCM of 14 and 15.
Which of the following is the LCM of 14 and 15? 45, 210, 15, 16
What is the Least Perfect Square Divisible by 14 and 15?
LCM of 14 and 15 = 2 × 3 × 5 × 7 [Incomplete pair(s): 2, 3, 5, 7] ⇒ Least perfect square divisible by each 14 and 15 = LCM(14, 15) × 2 × 3 × 5 × 7 = 44100 [Square root of 44100 = √44100 = ±210] Therefore, 44100 is the required number.
If the LCM of 15 and 14 is 210, Find its GCF.
Since the LCM of 15 and 14 = 210
⇒ 210 × GCF(15, 14) = 210
Therefore, the greatest common factor = 210/210 = 1.
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