Question

What is the LCM of sets of numbers 8, 12, 16, 36?

Answer 1

Hint: The given numbers are all even numbers. In order to find the LCM we will first find the factors of the given numbers. Then first we will take common factors and then the uncommon one. The product of these factors will be the LCM of the numbers above. This method will be the prime factors method.

Complete step by step answer:
We are given four numbers.
All four numbers are composite. So let’s factorize them first.
\[8 = 2 \times 2 \times 2\]
\[12 = 2 \times 2 \times 3\]
\[16 = 2 \times 2 \times 2 \times 2\]
\[36 = 2 \times 2 \times 3 \times 3\]
Now when we observe the numbers and their factors we can see that \[2 \times 2 = 4\]is the common factor.
From the remaining numbers the uncommon factors are \[2 \times 3 \times 2 \times 3\]
Thus the overall product that is the LCM is \[2 \times 2 \times 2 \times 2 \times 3 \times 3 = 144\]
 Thus the LCM of the set is 144.

Note:
Note that, LCM is the lowest common multiple. We can find LCM in many other ways also. But we will preferably use the prime factorization method. This method only uses prime numbers in the factor form. Also note that, we can use a tabular method also to find the LCM that also uses prime numbers.