LCM of 12 and 14

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The Least common multiple (LCM) is the smallest number that is divisible by the numbers 12 and 14. The LCM can be found using the listing multiples method, the prime factorization, and/or division methods. The LCM is used to find when two or more repeating events will occur together

What is the LCM of 12 and 14?

The LCM of 12 and 14 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 12 and 14?

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

LCM of 12 and 14 using the Listing Multiples Method

The LCM of 12 and 14 can be found using the following steps:
Step1: List the multiples of each number

Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108 …

Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, …

Step 2: Figure the smallest multiple from the listed multiples

The smallest common multiple is 84. Thus, LCM(12, 14) = 84.

LCM of 12 and 14 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: Devise prime factors of the given numbers:

Prime factorization of 12 = 2 × 2 × 3 = 2² x 3

Prime factorization of 14= 2 × 7

Step 2: Pick the highest powers of each prime factor:

Factors raised to their highest power = 22 x 3 x 7

Step 3:Find the product of the highest powers to get the LCM:

LCM(12, 14) = 22 x 3 x 7 = 84.

LCM of 12 and 14 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 get the LCM.

Step1: Write the numbers:

Step 2: Divide by common prime factors and multiply the divisors:

LCM of 12 and 14 = 2 x 2 x 3 x 7

Therefore, LCM = 84.

Important glossaries for LCM of 12 and 14

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.