Question

How do you find out the least common multiple of 15 and 2?

Answer 1

Hint: We shall find the multiples of the greater number one by one like first, second, third, fourth, fifth multiples and so on and see which multiple gets exactly divided by the smaller number. The multiple of the larger number which would be the first one to get completely divided by the smaller number will be termed as the lowest common factor of the two numbers.

Complete step-by-step solution:
We know that the bigger number out of 15 and 2 is 15
Thus, we shall start writing the multiples of 15 and check whether they are completely divisible by 2 or not.
The first multiple of 15 is given by multiplying 15 by 1.
 $\Rightarrow 15\times 1=15$
Thus, the first multiple of 15 is 15 itself.
Now, on dividing 15 by 2, we get
$\Rightarrow \dfrac{15}{2}=7.5$
However, since 15 is not completely divisible by 2, therefore, 15 is not the least common multiple.
The second multiple of 15 is given by multiplying 15 by 2.
 $\Rightarrow 15\times 2=15$
Thus, the second multiple of 15 is 30.
Now, on dividing 30 by 2, we get
$\Rightarrow \dfrac{30}{2}=15$
Since, 30 is completely divisible by 2, therefore, 30 is the least common multiple.
Therefore, the least common multiple of 15 and 2 is 30.

Note: There is another way of finding the least common multiples of the given numbers. We can perform the prime factorization of these numbers and the smallest number whose prime factorization has all the common factors of both the given numbers will be termed as the least common multiple of the two given numbers.