LCM of 12 and 18

The LCM of 12 and 18 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.

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

The LCM of 12 and 18 can be found using the following steps:

Steps:

1. List the multiples of each number

   — Multiples of 12 = 12, 24, 36, 48, 60, 72, …

   — Multiples of 18 = 18, 36, 54, 72, 90, …

2. Figure the smallest multiple from the listed multiples

  — The smallest common multiple is 36.

Thus, LCM(12, 18) = 36

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. Devise prime factors of the given numbers:

  — Prime factorization of 12 = 2 × 2 × 3

  — Prime factorization of 18 = 2 × 3 × 3

2.  Pick the highest powers of each prime factor:

  — Highest power of 2 = 2²

  — Highest power of 3 = 3²

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

     LCM(12, 18) = 2² × 3² = 36.

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.

Steps:

1.  Write the numbers:  

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

  — 2 × 2 × 3 × 3 = 36

Thus, LCM(12, 18) = 36.

• 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.