316 LearnersLast updated on May 26th, 2025
LCM of 6 and 9
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 6 and 9. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
What is the LCM of 6 and 9?
The LCM of 6 and 9 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.
How to find the LCM of 6 and 9?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 6 and 9 using the Listing multiples method
The LCM of 9 and 9 can be found using the following steps:
Steps:
1. Write down the multiples of each number:
Multiples of 6 = 6,12,18,…
Multiples of 9= 9,18,27,36…
2. Ascertain the smallest multiple from the listed multiples
Of the numbers 6 and 9, 18 is the least common multiple.
LCM of 6 and 9 using the Prime Factorization
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Steps:
1. Find the prime factors of the numbers:
Prime factorization of 6= 2×3
Prime factorization of 9 = 3×3
2. Multiply the highest power of each factor ascertained to get the LCM:
LCM (6,9) = 2×3×3 = 18
LCM of 6 and 9 using the Division Method
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Steps:
1. Write down the numbers in a row
2. A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers.
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.
4. The LCM of the numbers is the product of the prime numbers in the first column, i.e,
2×3×3= 18
LCM (6,9) = 18
Common Mistakes and how to avoid them while finding the LCM of 6 and 9
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 6 and 9, make a note while practicing.
Mistake 1
Confusing between LCM and HCF of the numbers 6 and 9.
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 6 and 9 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.
Mistake 2
Skipping the prime factors of the given numbers.
Errors in prime factorization often include incorrectly factoring 6 and 9. To illustrate, factoring 9 as 33 instead of 3×3. Doing so will yield the wrong LCM.
Mistake 3
Recognize that the numbers 6 and 9 are not relatively prime
Relatively prime numbers share no common factors but themselves and 1. In the case of 6 and 9 common factors are shared, so familiarize yourself with the concept of prime factors to make the process of finding the LCM of the given numbers easier.
LCM of 6 and 9 Examples
Problem 1
The gardener waters the vegetable section every 9 days and the fruit section every 6 days. If he waters both sections today, after how many days will he water both sections on the same day ?
LCM(6,9) = 18
Explanation
The gardener will water both the fruit and vegetable section in 18 days, 18 is the LCM of the digits 6 and 9, which in the given case expresses the smallest time interval between the numbers.
Problem 2
The gardener waters the vegetable section every 9 days and the fruit section every 6 days. If he waters both sections today, after how many days will he water both sections on the same day ?
LCM(6,9) = 18.
Explanation
The gardener will water both the fruit and vegetable section in 18 days, 18 is the LCM of the digits 6 and 9, which in the given case expresses the smallest time interval between the numbers.
Problem 3
Machine X stops for maintenance every 9 hours, while machine Y stops every 6 hours. In how long will the machines stop again?
LCM(6,9) = 18.
Explanation
The machines will stop together in 18 hours. 18 is the LCM of the digits 6 and 9, which in the given case expresses the smallest time interval between the numbers.
Problem 4
The LCM of a and b is 18 and their HCF is 8, what is the product of a and b?
We can use the below formula;
LCM(a,b)×HCF(a,b) =a×b
LCM(a,b)= 18, HCF(a,b) =3
a×b=18×3 = 54
Explanation
By following the above steps, we obtain the product of numbers a and b, which is 54.
Problem 5
The LCM of a and b is 18 and the product of a and b is 54, find the HCF of a and b.
LCM(a,b)×HCF(a,b) =a×b
LCM(a,b)= 18, a×b =54
18×HCF(a,b) =54
HCF(a,b) =54/18 = 3
Explanation
By using the above formula, we can find the HCF of any two numbers with just their LCM and the product.
FAQ’s on LCM of 6 and 9
1.Why is the LCM of 6 and 9 not simply their product (9 × 6 = 54) ?
2.What is the relationship between the Greatest Common Divisor (GCD)/ Highest Common Factor (HCF) and LCM of 6 and 9?
3. What is the LCM of 3,6,9 and 12?
4.What is the LCM of 6,9,12 and 18?
Important glossaries for LCM of 6 and 9
- 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.
