Question

What is the least common multiple of $6$ and $16$ ?

Answer 1

Hint: For these kinds of questions, we have two ways to do it. Before seeing how to do, let us try to understand what least common multiple or LCM mean. Multiples of a number are nothing but the numbers we obtain when that particular number is multiplied with $1,2,3,4,5,6,7,8,9,10.......$. These are called the multiples of a number So the least common multiple is the smallest multiple which is common with two different numbers.

Complete step by step solution:
For example, I have $2,3$. The multiples of $2$ are $2,4,6,8,10,12,14....$ . And the multiples of $3$ are $3,6,9,12,15,18....$ . As we can $6,12,18$ and so many other multiples are common to $2,3$. But the least common multiple to $2,3$ is $6$ because it is the smallest multiple .
This is one way to find out the least common multiples of two numbers. The other way to find out is prime factorization.
But let us solve this question using the first method.
The multiples of $6$ are $6,12,18,24,30,36,42,48,54,60.....$ . The multiples of $16$ are $16,32,48....$ . As we can see, $48$ is the least common multiple of $6,16$.

Note: Least common factor is not to be confused with highest common factor. They are both different. Using prime factorization, we write the given numbers in the product of prime numbers. After writing them as a product of prime factors, we check the common numbers. After that, we see which number gave us the highest exponent of the common multiple . We later multiply common multiple with highest exponent with other common multiples with highest exponent.