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206 LearnersLast updated on November 30th, 2024
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
LCM of 15 and 18 Examples
Problem 1
LCM (a, b) = 90. a=15. Find b.
Explanation
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)
Explanation
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?
Explanation
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?
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
: She loves to read number jokes and games.
