LCM of 2 and 9
2026-02-28 10:31 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-2-and-9

381 Learners

Last updated on August 5, 2025

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?

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:

  1. 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, …

  1. Ascertain the smallest multiple from the listed multiples:

  — The smallest common multiple is 18.

Thus, LCM(2, 9) = 18.

Explore Our Programs

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:

  1.  Find the prime factors of each number:

  — Prime factorization of 2 = 2

  — Prime factorization of 9 = 3 × 3

  1.  Take the highest powers of each prime factor:

  — Highest power of 2 = 2¹

  — Highest power of 3 = 3²

  1. 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:

  1.  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.

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

 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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

FAQs on LCM of 2 and 9

1.Why is the LCM of 2 and 9 not simply their product (2 × 9 = 18)?

 Multiplying gives you the product of the numbers, in this case,18. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method.

2.How do you find the LCM with different bases in an exponential equation ?

You can find the LCM For exponential equations with different bases by following the below example,

  • Find the LCM of 24×92 and 23×93
  • Factorize the terms and find the highest power 

Highest power of 2 =  24

Highest power of 9=  93

LCM =  24 × 93

3.What is the LCM formula using the HCF?

  • The LCM can be found using the formula, and as explained with the example given below. 

LCM (a, b)= a×b/HCF(a, b)

For 2 and 9, HCF(2,9)= 1

So, LCM(2,9)=2×9/1 = 18

4.What is the HCF of 2 and 9?

  • HCF of 2 and 9 can be found by following the below steps; 
  1. List down the prime factors of the numbers
  • Prime factors of 2 =  2
  • Prime factors of 9 = 3×3/32
  1. Find the common prime factors —> None 
  2. HCF of 2,9 = 1, as there are no common factors, the HCF of the given numbers is 1. 

5.What do the numbers 2 and 9 have in common?

  • 2 and 9 do not have any common factors, except 1, which is also the HCF of the numbers. 
  • 2 is a prime number, and prime numbers are characterized by have no common factors but 1. 
  • Factors of 9 are 3×3/32, sharing no factors with 2. 

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.

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.