Question

What is the lowest common multiple of 12 and 15.

Answer 1

Hint: We are given a question to find the lowest common multiple of two numbers 12 and 15. We will start by writing their factors. Then, we will write the lowest common multiple of 12 and 15 as the product of the factors which are not common in either of the numbers and the factors which are common in both is written only once. Hence, we will have the LCM of the given numbers 12 and 15.

Complete step by step answer:
According to the given question, we have to find the lowest common multiple of 12 and 15.
We will start by writing the factors of each of the numbers 12 and 15. We have,
\[12=2\times 2\times 3\]
And \[15=3\times 5\]
\[LCM(12,15)\]is done as follows,
In the factorization of 12, there are 2 twos’, so we will write that in LCM, we get,
\[LCM(12,15)=2\times 2\]
Next, we can see that 3 is present as a factor in both 12 and 15, so in the LCM we will write it only once, we have,
\[LCM(12,15)=2\times 2\times 3\]
Next, in the factorization of 15, we have a factor 5, and so we write this too in the LCM. And we have,
\[LCM(12,15)=2\times 2\times 3\times 5\]
\[\Rightarrow LCM(12,15)=60\]

Therefore, the \[LCM(12,15)=60\].

Note: We often finish off finding the LCM by multiplying the terms directly, that is, \[12\times 15=180\] but that is not the LCM, the question was to find the lowest possible, multiplying the numbers directly won’t lead us to the lowest multiple always.