LCM of 14 and 15
2026-02-28 17:23 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-14-and-15

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Last updated on August 5, 2025

The meaning of least common factor (LCM) is to find the smallest number that divides any two integers evenly. LCM is used mainly in fractions to find a common number for both the integers. We use LCM for solving problems, lining up cycles or even synchronizing of events, also to schedule tasks in everyday life.

What is the LCM of 14 and 15?

We use LCM of 14 and 15 to find  the smallest number that divides both the numbers equally.  The smallest positive number is the number that divides both numbers equally, is 210 without leaving any remainder. LCM is used mainly in fractions to find a common number for both the integers.

How to find the LCM of 14 and 15?

LCM of 14 and 15 using Division method:

In division method, we divide both the numbers, we begin with dividing side by side the smallest number. We continue dividing until we get a common number that divides both the numbers equally. It makes it easier for the children to focus on prime factors and identify them.

  • 2 divides 14 and not 15
  • 3 divides 15 and not 14
  • 5 divides 15 and not 14
  • 7 divides only 14.

Now multiply the divisors : 2×3×5×7=210 which is the LCM.
 

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LCM of 14 and 15 using Listing multiples:

Start by listing multiples of both the numbers separately:


Multiples of 14 are 14,28,42,56,70,84,98,112,126,140…..


Multiples of 15 are 15,30,45,60,75,90,105,120,135,150…..

The least common factor from the list is 210. Therefore, the LCM of 14 and 15 is 210.
 

LCM of 14 and 15 using Prime factorization:

We part both the numbers unto factors:


Factor of 14: 2×7


Factors of 15: 3×5

Take the powers of both the numbers and multiply together:


LCM=2x3x5x7=210.
 

Common Mistakes and How to Avoid Them in LCM of 14 and 15

While solving problems based on the LCM of 14 and 15, children fail to understand few concepts, to give an idea of the mistakes,    given below are a few mistakes and solutions of how to avoid them:
 

Problem 1

Add the fractions 2/14 and 3/15

Okay, lets begin

To add the fractions, we need to  find the common denominator, and we need to find the LCM of the numbers (14 and 15)

LCM of 14 and 15


Prime factors of 14: 2×7


Prime factors of 15: 3×5

 LCM = 2×3×5×7=210


2/14, multiply both numerator and denominator with 15 to get 210 as the denominator.


3/15, multiply both numerator and denominator with 14 to get 210 as the denominator.


We get, 30+42/210= 72/210.
 

Explanation

So the sum of 2/14 and 3/15 is 72/210.

Well explained 👍

Problem 2

Solving for x to add the fractions. x/14 + x/15=1

Okay, lets begin

 x/14 + x/15=1


  x/14, multiply both numerator and denominator with 15 to get 210 as the denominator, we get 15x/210.


  x /15, multiply both numerator and denominator with 14 to get 210 as the denominator, we get 14x/210.

14x+15x/210=1


14x+15x=1x210


29x=210


x=210/29
 

Explanation

So, the value of x is 210/29.
 

Well explained 👍

Problem 3

Add the fractions 5/14 and 6/15

Okay, lets begin

To add the fractions, we need to  find the common denominator, we need to find the LCM of the numbers 14 and 15.

LCM of 14 and 15


Prime factors of 14: 2×7


Prime factors of 15: 3×5


LCM = 2×3×5×7=210


5/14, multiply both numerator and denominator with 15 to get 210 as the denominator.


 6/15, multiply both numerator and denominator with 14 to get 210 as the denominator.


We get, 75+90/210= 165/210.
 

Explanation

So the sum of 5/14 and 6/15 is 165/210.
 

Well explained 👍

Problem 4

A student organization meets every 14 days, and the parent-teacher organization meets every 15 days. When will both the organization meet together again?

Okay, lets begin

LCM of 14 and 15


Prime factors of 14: 2×7


Prime factors of 15: 3×5


LCM = 2×3×5×7=210
 

Explanation

Both organizations will meet together every 210 days.
 

Well explained 👍

Problem 5

Solving for x to add the fractions. 6x/14 + 7x/15=1

Okay, lets begin

6x/14 + 7x/15=1


6x/14, multiply both numerator and denominator with 15 to get 210 as the denominator, we get 90x/210.


7x /15, multiply both numerator and denominator with 14 to get 210 as the denominator, we get 98x/210.

90x+98x/210=1


90x+98x=1x210


188x=210


x=210/188
 

Explanation

So, the value of x is 210/188.
 

Well explained 👍

FAQ’s on LCM of 14 and 15

1.What are the multiples of 128?

 The multiples / factors of 128 are given in pairs.


(1 and 128), (2 and 64), (4 and 32), (8 and 16).
 

2.There are how many factors in 3600?

There are 45 factors of 3600, but the prime factors are 2,3,5

3.Write the LCM of 12,15, and 45?

Prime factorization of 12 = 22×3


Prime factorization of 15 = 5×3


 Prime Factorization of 45 =5×32


LCM (12,15,45) = 32×22×5 = 180
 

4.Write six hundred and forty thousand in numbers?

‘Six hundred forty thousand’ is written as 640,000 in numbers.
 

5.What is the GCF, If the LCM of 14 and 15 is 210?

Important glossaries on the LCM of 15 and 14

  • Prime Factor: A natural number or whole number which has factors that are 1 and itself. For Example, 3 is a prime number.
  • Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. For example, the factorization of 14 is 2x7.
  • Co-prime numbers: numbers which has the only positive divisor of them both as 1. For example, 6 and 7.
     

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.