205 LearnersLast updated on May 26th, 2025
LCM of 2 and 9
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 2 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 2 and 9?
The LCM of 2 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.
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How to Find the LCM of 2 and 9?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 2 and 9 using the Listing Multiples Method
The LCM of 2 and 9 can be calculated using the following steps:
Steps:
- Write down the multiples of each number
— Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …
— Multiples of 9 = 9, 18, 27, 36, 45, 54, …
- Ascertain the smallest multiple from the listed multiples:
— The smallest common multiple is 18.
Thus, LCM(2, 9) = 18.
LCM of 2 and 9 using the Prime Factorization Method
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Steps:
- Find the prime factors of each number:
— Prime factorization of 2 = 2
— Prime factorization of 9 = 3 × 3
- Take the highest powers of each prime factor:
— Highest power of 2 = 2¹
— Highest power of 3 = 3²
- Multiply the highest powers to get the LCM:
LCM(2, 9) = 2¹ × 3² = 18.
LCM of 2 and 9 using the Division Method
This method involves dividing both numbers by their common prime factors and multiplying the divisors to find the LCM.
Steps:
- Write the numbers, divide by common prime factors and multiply the divisors.
Thus, LCM(2, 9) = 18
Common Mistakes and how to avoid them while finding the LCM of 2 and 9
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 2 and 9 make a note while practicing.
Mistake 1
Listing incorrect/overlooking multiples for the given numbers 2 and 9
This can be avoided by always double-checking the multiples of the numbers 2 and 9 and by not stopping too early. To elaborate, listing 2,4,8 as multiples of 2 and 9,18 as multiples of 9 and assuming 4 is the LCM.
Mistake 2
Confusing between LCM and HCF of the numbers 2 and 9
This can be avoided by learning that the LCM deals with multiples of the numbers 2 and 9, while HCF focuses on divisors of, 2 and 9, i.e., the HCF of 2 and 9 is 1, and the LCM is 18.
Mistake 3
Multiplying the numbers directly
Incorrectly assuming that multiplying the numbers 2 and 9 and assuming the product is the LCM instead of finding the lowest multiple.
Mistake 4
Skipping the LCM in the list method
Often, the first common multiples in the list of multiples are ignored due to an oversight, like 18 that appears on the list of both 2 and 9.
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LCM of 2 and 9 Examples
Problem 1
P visits a café every 2 and Q visits the same every 9 days. On which day are they likely to run into each other?
The LCM of 2 and 9 is 18.
Explanation
They will run into each other on the 18th day. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.
Problem 2
An HP Printer prints a batch every 2 minutes and a Canon printer prints a batch every 9 minutes. If the machines start at 10:00 AM, when will they print out a batch at the same time?
The LCM of 2 and 9 is 18.
Explanation
Both machines will print a batch together at 10:18 AM. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.
Problem 3
In a neighborhood park, the fountain show is turned on every 2 minutes, and the light show every 9 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?
The LCM of 2 and 9 is 18.
Explanation
Both the shows will turn on at the same time in 18 minutes. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.
Problem 4
A car mechanic services a red car every 2 days and a blue car every 9 days. If the cars are serviced today, when will they be serviced next together?
The LCM of 2 and 9 is 18.
Explanation
Both cars will be serviced again in 18 days. The LCM of 2 and 9 is 18, which is the smallest common time interval for the given digits.
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FAQs on LCM of 2 and 9
1.Why is the LCM of 2 and 9 not simply their product (2 × 9 = 18)?
2.How do you find the LCM with different bases in an exponential equation ?
3.What is the LCM formula using the HCF?
4.What is the HCF of 2 and 9?
5.What do the numbers 2 and 9 have in common?
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Important glossaries for the LCM of 2 and 9
- 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.
