Question

How do you find the least common multiple of $24,32$?

Answer 1

Hint: To find the least common multiple (L.C.M) of two numbers you have to remember the definition of L.C.M. Least common multiple (L.C.M) of two numbers is a number which is multiple of the both numbers and also it is the smallest such multiple of both numbers. For example $6$ and $12$ are multiple of both $2$ and $3$ but $6$ is the least common multiple and $12$ is just a multiple.

Complete step by step solution:
In this question we are required to find the least common multiple (L.C.M) of$24,32$. We can find L.C.M of two numbers by two methods.
1. By finding the multiples
2. By prime factorization method

1. By finding the multiple:
To find the least common multiple (L.C.M) by finding the multiples we write the first n multiples of both the numbers and find for the least multiple which is common in both the numbers.
First $5$ multiples of $24 = 24,48,72,96,120$
First $5$ multiples of $32 = 32,64,96,128,160$
Now we will find for common and least multiple, $96$ is the number which is multiple of both $24,32$.

Hence least common multiple (L.C.M) of $24,32$ is $96$.

2. By prime factorization method:
In this method we will first write both numbers in the form of their prime factors individually and multiply the common pairs of both the numbers to get the L.C.M.
Prime factorization of $24 = 2 \times 2 \times 2 \times 3$
Prime factorization of $32 = 2 \times 2 \times 2 \times 2 \times 2$
Now we will write prime factors of both the numbers together, which gives
$ = 2 \times 2 \times 2 \times 3 \times 2 \times 2 \times 2 \times 2 \times 2$
Now we will pair the common prime factors to write it once. So it becomes
$2 \times 2 \times 2 \times 2 \times 2 \times 3$ this is the L.C.M simplifying it we get,
$2 \times 2 \times 2 \times 2 \times 2 \times 3 = 96$
Least common multiple (L.C.M) of $24,32$ $ = 96$.

Note: We have solved this question with two methods of finding Least common multiples (L.C.M). For finding the least common multiple prefer to use the prime factorization method because in finding the least common multiple by using multiples could be lengthy we could end up writing first $15,20$or more multiples. So please prefer the prime factorization method to find L.C.M.