Question

What is the least common multiple of 9 and 15?

Answer 1

Hint: The given question is based on finding the least common multiple of the two 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 two numbers are the same, then we will take it once only. Hence, we will have the LCM of the given numbers.

Complete step by step answer:
According to the given question, we have to find the LCM or Least Common Multiple of the numbers 9 and 15.
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 9 and 15.
The factors of the numbers, we have,
$$9=3\times 3$$
$$15=3\times 5$$
We can see that the factors of 9 and 15 have 3 in common so, we will take 3 once only in the LCM. Next, there is one 3 in the factor of 9 and one 5 in the factor of 15, so we will take that as well.
So, the LCM of the given numbers, we get,
$$LCM(9,15)=3\times 3\times 5=45$$

Therefore, the LCM of the given numbers is 45.

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, 9 and 15 is 3.