LCM of 3 and 4

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The Least common multiple (LCM) is the smallest number that is divisible by the numbers 3 and 4. 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 3 and 4?

The LCM of 3 and 4 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 3 and 4?

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

LCM of 3 and 4 using the Listing Multiples Method

The LCM of 3 and 4 can be found using the following steps:

Step 1:Write down the multiples of each number

Multiples of 3 = 3, 6, 9,12 …

Multiples of 4 = 4, 8,12 …

Step 2: Ascertain the smallest multiple from the listed multiples

The least common multiple is 12.

LCM of 3 and 4 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.

Step1: Find the prime factors of the numbers:

Prime factorization of 3 = 3

Prime factorization of 4 = 2 × 2

Step2:Take the highest powers of each prime factor:

Multiply the highest powers to get the LCM

LCM(3, 4) = 12

LCM of 3 and 4 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: continue the division till we reach to 1.

3 ×2 ×2 =12

Thus, LCM(3, 4) = 12

Important glossaries for the LCM of 3 and 4

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.