Question

How do you find the Least common multiple of 27, 18?

Answer 1

Hint: This problem deals with finding the least common multiple of the given two numbers. Least common multiple is also abbreviated as LCM which stands for the least common multiple. Here in order to find the least common multiple of the given numbers we divide the numbers with their least common factor until we get prime numbers.

Complete step-by-step solution:
The least common multiple of these numbers which are 27 and 18 is the common multiple of these two numbers which is the least of all the common multiples of these two numbers which are 27 and 18.
Here dividing the two numbers 27 and 18 with 3 as shown below:
$\Rightarrow {\displaystyle \frac{27}{3}},{\displaystyle \frac{18}{3}}=9,6$
Now the obtained numbers after division by 3 are still divisible by 3, hence again dividing the obtained numbers by 3, as shown below:
$\Rightarrow {\displaystyle \frac{9}{3}},{\displaystyle \frac{6}{3}}=3,2$
Now these two obtained numbers are prime numbers hence are not divisible any other numbers except 1.
So now the least common multiple would be the product of the numbers 3, 3, 3 and 2.
So the least common multiple of the given two numbers 27 and 18 are given below:
$\Rightarrow 3\times 3\times 3\times 2=54$
So the LCM of 27 and 18 is equal to 54.

Note: Please note that we found the LCM of the given two numbers by the process of cascades of dividing the numbers by the least common mutual factors till we get the prime factors. At last the LCM of the numbers is the product of all these factors including the prime factors.