157 LearnersLast updated on May 26th, 2025
LCM of 15 and 27
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 15 and 27?
We use LCM of 15 and 27 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 15 and 27?
The LCM of 15 and 27 can be found by the following methods like division method, listing multiples, prime factorization.
LCM of 15 and 27 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.
- 3 divides 15 and 27
- 5 divides 15 and not 27
- 9 divides 27 and not 15
Now multiply the divisors : 3×5×9=135 which is the LCM.
LCM of 15 and 27 using Listing multiples:
Start by listing multiples of both the numbers separately:
Multiples of 15 are 15,30,45,60,75,90,105,120,135…..
Multiples of 27 are 27,54,81,108,135…..
The least common factor from the list is 135. Therefore, the LCM of 15 and 27 is 135.
LCM of 15 and 27 using Prime factorization:
We part both the numbers unto factors:
Factor of 15: 3×5
Factors of 27: 33
Take the powers of both the numbers and multiply together:
LCM=33x5=135.
Common Mistakes and How to Avoid Them in LCM of 15 and 27
While solving problems based on the LCM of 15 and 27, 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.
LCM of 15 and 27 Examples
Problem 1
Find the LCM of 15 and x, if the LCM is 60. What is the value of X?
X=4.
Explanation
To add the fractions, we need to find the prime factorization of 15
Prime factors of 15: 3 × 5
The LCM of 15 and X is given as 60.
60= 22 x3x5
Since X shares factors with 60, the missing number should include 22 as 15 does not include any factor of 2.
Therefore,
X=22=4.
LCM of 15 and 4 is :
LCM(15,4)= 22 × 3 × 5 =60.
Thus, X=4.
Problem 2
Given two pairs of numbers (12,18) and (15,24) which pair has the greater LCM?
let us first find LCM of each pair:
LCM of 12 and 18:
Factorization of 12= 22 × 3
Factors of 18= 2x 32
Take the highest powers of both the numbers:
LCM(12,18)= 22 × 32 = 4 × 9=36
LCM of 15 and 24:
Factorization of 15= 3 × 5
Factorization of 24= 23 × 3
Take the highest powers of both the numbers:
LCM(15,24)= 23 × 3 × 5= 8 × 15=120.
Explanation
LCM(15,24)= 120
LCM(12,18)= 36
so, (15,24 has greater LCM
Problem 3
Simplify the fraction 15/27 by finding the LCM of the numerator and the denominator’s greatest common divisor(GCD).
answer : 5/9
Explanation
Prime Factorization of 15:
15=3 × 5
Prime Factorization of 27:
27=33
GCD of 15 and 27 is 3.
To simplify:
15/27 = 15÷3/27÷3 = 5/9.
Problem 4
If the LCM of two numbers a and b is 72, and their GCD is 4. Find the product of a and b.
product of a and b =288
Explanation
LCM(a, b) x GCD (a, b)= a × b
LCM(a, b)=72 and GCD(a, b)=4
72 × 4= a × b
a × b =288.
Problem 5
If a=18 and LCM of a and b is 90, find b.
b=10.
Explanation
by using the formula:
LCM(a, b)= a × b/GCD(a, b)
18=2x32 and the LCM is 90
Factors of 90 are 2 × 32 × 5
The missing factor is 5, so b =5 × 2 =10
b=10.
FAQs on LCM of 15 and 27
1.What is the LCM of 18 and 27?
2.There are how many factors in 3600?
3.Write the LCM of 15,18,24,27 and 56 ?
4.What is the LCM of 8,14 and 9?
5.If the LCM of two numbers a and b is 840, and one of the numbers is 28, find the smallest possible value of b?
6.How can children in Qatar use numbers in everyday life to understand LCM of 15 and 27?
7.What are some fun ways kids in Qatar can practice LCM of 15 and 27 with numbers?
8.What role do numbers and LCM of 15 and 27 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve LCM of 15 and 27 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 2×7.
- Co-prime numbers: numbers which have 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
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