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Last updated on September 23rd, 2024
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 9 and 12. 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 9 and 12 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 9 and 12 can be found using the following steps;
Steps:
1. Write down the multiples of each number:
Multiples of 9= 9,18,27,36…
Multiples of 12 = 12,24,36…
2. Ascertain the smallest multiple from the listed multiples of 9 and 12.
The LCM (Least common multiple)
The least common multiple of the numbers 9 and 12 is 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. Find the prime factors of the numbers:
Prime factorization of 9 = 3×3
Prime factorization of 12 = 2×2×3
2. Multiply the highest power of each factor ascertained to get the LCM:
LCM (9,12) = 2×2×3×3 = 36
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Steps:
1. Write down the numbers in a row;
2. A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers.
3. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
4. The LCM of the numbers is the product of the prime numbers in the first column, i.e,
2×2×3×3= 36
LCM (9,12) = 36