Question

What is the least common multiple of 3, 2 and 15?

Answer 1

Hint: Least common multiple of two numbers means the smallest number that is multiple of both the numbers. So, to find the L.C.M of 3, 2 and 15 write the multiples of all three numbers and then find the smallest common multiple from them.

Complete step by step solution:
In this question, we are given 3 numbers 3, 2 and 15 and we have to find their least common multiple.
First of all, what is the least common multiple?
Least common multiple of two numbers also known as L.C.M is the smallest number that is a multiple of both the given numbers. For example: 2 and 3. Now, the multiples of 2 are 2, 4, 6… and multiples of 3 are 3, 6, 9… Here, the smallest common multiple between these two numbers is 6. Hence, the L.CM of 2 and 3 is 6.
Here, we have to find the smallest number that is a multiple of 3, 2 and 15.
Finding L.C.M using multiples:
First, write the multiples of 2.
 $ \to $ Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30…
 $ \to $ Multiples of 3: 3, 6, 9, 15, 18, 21, 24, 27, 30, 33, 36…..
 $ \to $ Multiples of 15: 15, 30, 45, 60, 75, 90…..
Here, we can see that the least common multiple between 2, 3 and 15 is 30.
Therefore, the L.C.M of 2, 3 and 15 is 30.
So, the correct answer is “30”.

Note: We can also find the L.C.M using the prime factorization method.
Write the prime factors of all the three numbers.
 $
  2 = 2 \times 1 \\
  3 = 3 \times 1 \\
  15 = 3 \times 5 \;
  $
Now, if a number is repeated more than once, then multiply it only once.
Therefore, L.C.M of 2, 3 and 15 $ = 2 \times 3 \times 5 = 30 $