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157 LearnersLast updated on November 29th, 2024
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.
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
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?
Explanation
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?
Explanation
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?
Explanation
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?
Explanation
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?
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.
