148 LearnersLast updated on May 26th, 2025
LCM of 14 and 15
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?
The LCM of 14 and 15 can be found by the following methods like division method, listing multiples, prime factorization.
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.
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:
Mistake 1
Stopping the division method way too soon.
Students sometimes stop dividing very soon, when they are not able to divide both the numbers with the same number. For example, we can divide14 by 2, but 15 isn't divisible by 2. To continue the dividing method until all the factors are found. The students should continue dividing until they find the common number that divides both the integers.
Examples of LCM of 14 and 15
Problem 1
Add the fractions 2/14 and 3/15
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.
Problem 2
Solving for x to add the fractions. x/14 + x/15=1
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.
Problem 3
Add the fractions 5/14 and 6/15
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.
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?
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.
Problem 5
Solving for x to add the fractions. 6x/14 + 7x/15=1
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.
FAQ’s on LCM of 14 and 15
1.What are the multiples of 128?
2.There are how many factors in 3600?
3.Write the LCM of 12,15, and 45?
4.Write six hundred and forty thousand in numbers?
5.What is the GCF, If the LCM of 14 and 15 is 210?
6.How can children in India use numbers in everyday life to understand LCM of 14 and 15?
7.What are some fun ways kids in India can practice LCM of 14 and 15 with numbers?
8.What role do numbers and LCM of 14 and 15 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve LCM of 14 and 15 skills?
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
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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.
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