161 LearnersLast updated on May 26th, 2025
LCM of 11 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 11 and 15?
We use LCM of 11 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 165 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 11 and 15?
The LCM of 11 and 15 can be found by the following methods like division method, listing multiples, prime factorization.
LCM of 11 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.
- 11 is a prime number and cannot be divided further.
- 3 divides 15 and not 11.
- 5 divides 15 and not 11
Now multiply the divisors : 11×3×5=165, which is the LCM.
LCM of 11 and 15 using Listing multiples:
Step 1: Start by listing multiples of both the numbers separately:
Multiples of 11 are 11,22,33,44,55,66,77,88,99,110,121,132,143,154,165…..'
Multiples of 15 are 15,30,45,60,75,90,105,120,135,150,165…..
Step 2: The least common factor from the list is 165. Therefore, the LCM of 11 and 15 is 165.
LCM of 11 and 15 using Prime factorization:
Step 1:We part both the numbers unto factors:
Factor of 11: 11
Factors of 15: 3×5
Step 2:Take the powers of both the numbers and multiply together:
LCM=11x3x5=165.
Common Mistakes and How to Avoid Them in LCM of 11 and 15
While solving problems based on the LCM of 11 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 11 and 15
Problem 1
Add the fractions 2x/11 and 3x/15=1
To add the fractions, we need to find the common denominator, and we need to find the LCM of the numbers (11 and 15)
LCM of 11 and 15
Prime factors of 11: 11
Prime factors of 15: 3×5
LCM = 11×3×5=165
2x/11, multiply both numerator and denominator with 15 to get 165 as the denominator.
3x/15, multiply both numerator and denominator with 11 to get 165 as the denominator.
We get, 30x+33x/165=1
63x/165=1
63x=165
x=165/63=55/21
x=55/21.
Explanation
Answer :x=55/21.
Problem 2
Find the LCM of 11 and 15 to rewrite the mixed fractions 2 511 and 1215 with the same denominator.
Convert the mixed fractions to improper fractions:
Explanation
So the fractions are 405/165 and 187/165.
Problem 3
If x/11+5/15=1, find the value of x.
To add the fractions, we need to find the common denominator, we need to find the LCM of the numbers 11 and 15.
LCM of 11 and 15
Prime factors of 11: 11
Prime factors of 15: 3×5
LCM = 3×5×11=165
x/11 multiply both numerator and denominator with 15 to get 165 as the denominator.
5/15 Multiply both numerator and denominator with 11 to get 165 as the denominator.
We get, 15x + 55/165 = 1.
15x + 55=165
15x=165-55
x=110/15
x=22/3.
Explanation
Answer: x=22/3.
Problem 4
Use the division method to find the LCM of 11 and 15.
Divide the numbers by their prime factors:
Step 11 15
3 11 5
5 11 1
11 1 1
LCM = 3x 5 x11=165
Explanation
LCM of 11 and 15 = 3x 5 x11=165
Problem 5
If LCM(11,15)=165 and a × b=330, what is GCF (a, b)?
GCF (a, b)
= a x b / LCM (a,b)
= 330/165
=2.
Explanation
as we know LCM(11,15)=165.
FAQ’s on LCM of 11 and 15
1.What is the LCM of 15,11 and 12?
2.There are how many factors in 3600?
3.Write the LCM of 11,15, and 21?
4.Write six hundred and forty thousand in numbers?
5. What is the LCM of 17 and 19?
Important glossaries on the LCM of 15 and 11
- 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 2×7.
- Co-prime numbers: numbers which has the only positive divisor of them both as 1. For example, 6 and 7.
Explore More numbers
Previous to LCM of 11 and 15
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.
