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Last updated on September 17th, 2024
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 12 and 18. 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.
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:
— Multiples of 12 = 12, 24, 36, 48, 60, 72, …
— Multiples of 18 = 18, 36, 54, 72, 90, …
— 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:
— Prime factorization of 12 = 2 × 2 × 3
— Prime factorization of 18 = 2 × 3 × 3
— Highest power of 2 = 2²
— Highest power of 3 = 3²
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:
— 2 × 2 × 3 × 3 = 36
Thus, LCM(12, 18) = 36.