Question

What is the LCM of 4, 9, 12?

Answer 1

Hint: To find the LCM, you need to find the smallest number which can be divided by all the numbers in the question that is 4, 9 , 12 without any remainder. To do the process of LCM, we need to continue dividing all the numbers, that is 4, 9 and 12 with prime numbers until we get all ones in the end. To get the LCM, you need to multiply all the numbers in the left hand side.

Complete step by step solution:
Here is the step wise solution.
The first step to do is to divide all the numbers with prime numbers and keep doing it continuously till we get all ones in the end.
$2\left| \!{\underline {\,
  4,9,12 \,}} \right.$
$2\left| \!{\underline {\,
  2,9,6 \,}} \right.$
$3\left| \!{\underline {\,
  1,9,3 \,}} \right.$
$3\left| \!{\underline {\,
  1,3,1 \,}} \right.$
$1\left| \!{\underline {\,
  1,1,1 \,}} \right.$
After this we get all ones in the end. Therefore we stop the division. Now, we have to multiply all the numbers on the left side which are 2, 2, 3, 3. Therefore, multiplying them we get the answer as 36. Hence LCM of 4, 9, 12 is 36.
Therefore, we get the final answer of the question, what is the LCM of 4, 9, 12, as 36.

Note: You need to know how to do LCM. Also note that while doing the LCM, we only do the division using the prime numbers. You can also check if you got the correct answer by dividing the answer with all the numbers for which you found the LCM and see if it is divisible without any remainder.