LCM of 2 and 3

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The Least common multiple (LCM) is the smallest number that is divisible by the numbers 2 and 3. 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 3?

The LCM of 2 and 3 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 3?

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;

LCM of 2 and 3 using the Listing Multiples Method

The LCM of 2 and 3 can be found using the following steps:

Step 1: Write down the multiples of each number

Multiples of 2 = 2, 4, 6, 8, …

Multiples of 3 = 3, 6, 9, 12, 15, 18, …

Step 2: Ascertain the smallest multiple from the listed multiples

The least common multiple is 6.

LCM of 2 and 3 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.

Step 1: Find the prime factors of the numbers:

Prime factorization of 2 = 2

Prime factorization of 3 = 3

Step 2:Take the highest powers of each prime factor and multiply the highest powers to get the LCM:

LCM(2,3) = 6

LCM of 2 and 3 using the Division Method

This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.

Step 1: Write the numbers, divide by common prime factors and multiply the divisors.

Step 2: 2 and 3 are only prime factors in this case:

2 × 3 = 6

Thus, LCM(2,3) = 6

Important glossaries for the number of 2 and 3

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.