Question

Find the LCM of 3, 4 and 18

Answer 1

Hint: The least common multiple of a set of numbers is defined as the smallest possible number that is divisible by all the numbers in that set. To find the least common multiple of a set of numbers, we first factorize it, that is we write all the numbers as the product of the prime numbers (Prime numbers are those numbers that are divisible only by one and itself). This way, we can find out the least common multiple of 3, 4 and 18.

Complete step-by-step answer:
For finding out the least common multiple, we observe the prime factorization of the given set. The least common multiple is the product of prime factors occurring in the given set raised to the power the highest number of times each prime number has occurred.
Writing all the given numbers as a product of prime numbers, we get –
 $$\begin{gathered} 3=3 \\ 4=2\times 2 \\ 18=2\times 3\times 3 \end{gathered}$$
Now, we see that the highest occurrence of 2 is 2 times and that of 3 is also 2 times, so the least common multiple of 3, 4 and 18 is –
 $$\begin{gathered} LCM=2\times 2\times 3\times 3 \\ \Rightarrow LCM=36 \end{gathered}$$
Hence, 36 is the LCM of 3, 4 and 18.
So, the correct answer is “36”.

Note: For finding out the least common multiple, we observe the prime factorization of the given set. The least common multiple is the product of prime factors occurring in the given set raised to the power the highest number of times each prime number has occurred. For example, in the given set 2 and 3 are the involved prime numbers, so $LCM=2^n{3}^m$ , in the prime factorization of 4, 2 occurs 2 times which is the highest number of occurrence so n=2, and in the prime factorization of 18, 3 occurs 2 times so m=2. After calculating the LCM, we can check if the answer is correct or not by ensuring that the LCM is completely divisible by all the numbers of the set.