brightchamps-logo
hamburger

open_icon Table Of Contents

Table of Contents

LIGHT_BULB_MATHS_BLOG
scholar-purple-hat133 Learners

Last updated on November 29th, 2024

maths_whiteboard

LCM of 2 and 9

maths_mascot
Foundation
Intermediate
Advance Topics

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.

GREEN_BACKGROUND_HEADING_MASCOT

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.

GREEN_BACKGROUND_HEADING_MASCOT

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;

GREEN_BACKGROUND_HEADING_MASCOT

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.

GREEN_BACKGROUND_HEADING_MASCOT

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.

GREEN_BACKGROUND_HEADING_MASCOT

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

GREEN_BACKGROUND_HEADING_MASCOT

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.
GREEN_BACKGROUND_HEADING_MASCOT

Explore More numbers