Question

What is the least common multiple of 3, 4 and 6?

Answer 1

Hint: To obtain the least common multiple of the given number we will use a common division method. Firstly we will write all the numbers inside the division sign then start by dividing them with the smallest prime number separately till we get all remainder as 1. Finally multiply all the prime factors and get the desired answer.

Complete step-by-step answer:
The two numbers are given as 3, 4 and 6.
Now we will use the common division method as below:
$\begin{array}{rl}& 2|\underset{―}{3,4,6}\\ & 2|\underset{―}{3,2,3}\\ & 3|\underset{―}{3,1,3}\\ & 1,1,1\end{array}$
The factors obtained are the prime number on the left side which is:
$\{2,2,3\}$
Next we will multiply all the factors obtained as:
Least common multiple $=2\times 2\times 3$
Least common multiple $=13$
Hence LCM or least common multiple 3, 4 and 6 is 12.

Note: Least common multiple is also known as LCM of two or more numbers which is the smallest integer divided by all those number completely. It’s most important use is to simplify the fraction values by making the denominator term equal so that the numerator term can be added or subtracted. We can use the prime factorizing method where we find all the prime factors of all the number separately and then multiply the factors with the highest term from each of the values to get the LCM as follows:
Prime factor of 3 is given below:
$3=1\times 3$.….$\left(1\right)$
Prime factor of 45 is given below:
$4=1\times 2\times 2$
$4=1\times 2^2$…..$\left(2\right)$
Prime factor of 6 is given below:
$6=1\times 2\times 3$……$\left(3\right)$
Common factor from equation (1), (2) and (3) are:
$\begin{array}{rl}& \Rightarrow 1\times 2^2\times 3\\ & \Rightarrow 12\end{array}$
So the LCM of the number 3, 4 and 6 is 12 which is same as the above solution.