Question

What is the LCM of 4, 9 and 3?

Answer 1

Hint: The given question is based on finding the least common multiple of the three numbers given. We will first find the factors of the given numbers and then we will take those factors which are not common in the factors of the three numbers given and if two factors in the factors of the given three numbers are the same, then we will take it once only.

Complete step by step answer:
According to the given question, we have to find the LCM or Least Common Multiple of the numbers 4, 9 and 3.
LCM refers to Least Common Multiple or we can also use it as Least Common Divisor, LCD. If suppose we have to find the LCM of two numbers say ‘x’ and ‘y’, then the LCM will be the least positive number which is evenly divisible or is a multiple of both ‘x’ and ‘y’.
For example - \[LCM(5,10)=10\], as the factors of 5 and 10 had 5 in either of them so it was taken once and since 2 was not common it was taken as it is. That is, we have,
\[5=5\times 1\]
\[10=5\times 2\]
\[LCM(5,10)=5\times 2=10\]
The given question asked us to find the LCM of 4, 9 and 3.
The factors of the numbers, we have,
\[4=2\times 2\]
\[9=3\times 3\]
\[3=3\times 1\]
We can see that the factor of 4 which is 2 is not in any other number’s factors, so we take 4 in the LCM. Next, 3 is seen to be common in both the factors of 9 and 3 so here we will take it once only and there is one 3 in the factors of 9, we will take that as well.
So, the LCM of the given numbers, we get,
\[LCM(4,9,3)=2\times 2\times 3\times 3=36\]

Therefore, the LCM of the given numbers is 36.

Note: The LCM of the numbers may seem easy to find but one additional factor or one less factor if taken may result in the entire question going wrong. Also, do not confuse LCM with HCF. HCF of two numbers, say, 3 and 9 is 3.