139 LearnersLast updated on May 26th, 2025
LCM of 18 and 27
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 18 and 27. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycles of events.
What is the LCM of 18 and 27?
The LCM of 18 and 27 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 18 and 27 ?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 18 and 27 using the Listing multiples method
To ascertain the LCM, list the multiples of the integers until a common multiple is found.
Steps 1:Writedown the multiples of each number:
Multiples of 18 = 18,36,54,...
Multiples of 27 = 27,54,...
Step 2: Ascertain the smallest multiple from the listed multiples of 18 and 27.
The LCM (Least common multiple) of 18 and 27 is 54. i.e., 54 is divisible by 18 and 27 with no reminder.
LCM of 18 and 27 using the Prime Factorization
This method involves finding 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 18 = 2×3×3
Prime factorization of 27= 3×3×3
Take the highest power of each prime factor and multiply the ascertained factors to get the LCM:
LCM (18,27) = 54
LCM of 18 and 27 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 (18,27) = 54
Common Mistakes and how to avoid them in LCM of 18 and 27
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 18 and 27, make a note while practicing.
Mistake 1
Confusing between LCM and HCF of the numbers 18 and 27
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 18 and 27 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 18 and 27, Examples
Problem 1
Elaborate on the relationship between HCF and LCM of 18 and 27.
The relationship between HCF and LCM can be verified using this formula; HCF(a,b)×LCM(a,b) = a×b
HCF of 18,27 = 9
LCM of 18,27 = 54
Now apply the formula,
HCF(a,b)×LCM(a,b) = a×b
HCF(18,27)×LCM(18,27) = 18×27
9×54 = 18×27
486=486
Explanation
The above explains the relationship between the HCF and the LCM of 18 and 27. The given formula works to verify the relationship between the HCF and LCM for any given pair of numbers.
Problem 2
If the HCF of 18 and 27 is 9, using the relationship between 18 and 27, find the LCM.
Given values;
HCF = 9
a = 18
b = 27
Explanation
The relationship between HCF and LCM, as explained above allows us to find the LCM without direct calculation.
Problem 3
Trains A and B arrive every 27 minutes and 18 minutes at the station at the same time. In how long will they arrive together again?
The LCM of 18 and 27 =54
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 54 minutes.
FAQ’s on LCM of 18 and 27
1.List the common factors of 18 and 27.
2.What is the LCM of 18,27 and 36?
3.What is the LCM of 18,27 and 35?
4.What is the LCM of 18,20,24 and 27?
5.What is the LCM of 18 and 32?
6.How can children in Singapore use numbers in everyday life to understand LCM of 18 and 27 ?
7.What are some fun ways kids in Singapore can practice LCM of 18 and 27 with numbers?
8.What role do numbers and LCM of 18 and 27 play in helping children in Singapore develop problem-solving skills?
9.How can families in Singapore create number-rich environments to improve LCM of 18 and 27 skills?
mportant glossaries for LCM of 18 and 27
- 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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