Last updated on May 26th, 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.
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.
The LCM of 14 and 15 can be found by the following methods like division method, listing multiples, prime factorization.
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.
Now multiply the divisors : 2×3×5×7=210 which is the LCM.
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.
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.
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:
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.
So the sum of 2/14 and 3/15 is 72/210.
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
So, the value of x is 210/29.
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.
So the sum of 5/14 and 6/15 is 165/210.
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
Both organizations will meet together every 210 days.
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
So, the value of x is 210/188.
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.
: She loves to read number jokes and games.