212 LearnersLast updated on May 26th, 2025
LCM of 15 and 18
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 15 and 18. In daily life, we use application of LCM to synchronize two musical instruments playing 2 different beats.
What is the LCM of 15 and 18?
The LCM of 15 and 18 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations like addition and subtraction with fractions to equate the denominators.
How to find the LCM of 15 and 18 ?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 15 and 18 using the Listing multiples method
To ascertain the LCM, list the multiples of the integers until a common multiple is found.
Step 1: Writedown the multiples of each number:
Multiples of 15 = 15,30,45,60,75,90…
Multiples of 18 = 18,36,54,72,90,…
Step 2: Ascertain the smallest multiple from the listed multiples of 15 and 18.
The LCM (Least common multiple) of 15 and 18 is 90. i.e., 90 is divisible by 15 and 18 with no reminder.
LCM of 15 and 18 using the Prime Factorization
In this method we find the prime factors of each number and then multiplying the highest power of the prime factors to get the LCM.
Step 1: Find the prime factors of the numbers:
Prime factorization of 15 = 5×3
Prime factorization of 18 = 2×3×3
Step 2:Take the highest power of each prime factor and multiply the ascertained factors to get the LCM:
LCM (15,18) = 90
LCM of 15 and 18 using the Division Method
The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Step 1:Write down the numbers in a row;
Step 2:Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers.
Step 3:Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
Step 4:The LCM of the numbers is the product of the prime numbers in the first column, i.e.,
LCM (15,18) = 90
Common Mistakes and how to avoid them in LCM of 15 and 18
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 15 and 18, make a note while practicing.
Mistake 1
Confusing between LCM and HCF of the numbers 15 and 18
It is common for one to be confused between the HCF (Highest common factor) and LCM (least common multiple). LCM is the smallest number divisible by 15 and 18 while, the largest number that divides them both is the HCF.
A simple trick to remember is that the HCF is going to be a relatively smaller number than the LCM, as it deals with divisors
LCM of 15 and 18 Examples
Problem 1
LCM (a, b) = 90. a=15. Find b.
LCM (15,b) = 90
b is a divisor of 90, so we list the divisors of 90;
1,2,3,5,6,9,10,15,18,30,45,90.
Explanation
For the LCM to be 90, the missing number has to be 18, the LCM (15,18) = 90.
Problem 2
The LCM of 15 and 18 is x; find the value of x such that; x/HCF(15,18)=LCM(15,x)/HCF(x,18)
We know that;
LCM (15,18) = 90
HCF (15,18) = 3
Substituting the same in the given formula;
x/HCF(15,18)=LCM(15,x)/HCF(x,18)
90/3 = LCM(15,x)/HCF(x,18)
The same simplifies to;
30 = LCM(15,x)/HCF(x,18)
For x= 18, we know that
LCM (15,18) = 90
HCF (18,18) = 18
Explanation
From the above we can conclude that x = 18 on both sides holds true.
Problem 3
Trains A and B arrive every 15 minutes and 18 minutes at the station at the same time. In how long will they arrive together again?
The LCM of 15 and 18 = 90.
Explanation
The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the trains at the same time, which is in 90 minutes.
FAQ’s on LCM of 15 and 18
1.What is the HCF of 15 and 18?
2.What are the factors of 15 and 18?
3.What is the LCM of 15 and 8?
4.What is the LCM of 11 and 18?
5.What is the LCM of 12,15 and 18?
6.How can children in United States use numbers in everyday life to understand LCM of 15 and 18 ?
7.What are some fun ways kids in United States can practice LCM of 15 and 18 with numbers?
8.What role do numbers and LCM of 15 and 18 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 15 and 18 skills?
Important glossaries for LCM of 15 and 18
- Multiple: A number and any integer multiplied.
- Prime Factor: A natural number (other than 1) that has factors that are one and itself.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
- Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.
- Relatively Prime Numbers:Numbers that have no common factors other than 1.
- Fraction: A representation of a part of a whole.
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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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