Question

What is the LCM of sets of numbers 8, 12, 16, 3?

Answer 1

Hint: 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.
\[8 = 2 \times 2 \times 2\]
\[12 = 2 \times 2 \times 3\]
\[16 = 2 \times 2 \times 2 \times 2\]
\[3 = 3\]
Now when we observe the numbers and their factors we can see that there is no common factor directly but we can check for a set of numbers.
Thus common factors of 8,12 and 16 can be, \[2 \times 2\]
Now the uncommon factors are \[2 \times 2 \times 3\].
Now the one factor of 3 which is 3 is already taken into count.
Thus the overall product that is the LCM is \[2 \times 2 \times 2 \times 2 \times 3 = 54\]

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.
We can find LCM by alternative way:
We can take the maximum power of prime factors from the factors of given numbers.
For example- In the above factor there are 4 times we got 2 as a factor and once we got 3 so we can multiply to get the result.