Question

What is the least common multiple of 2, 3, 6?

Answer 1

Hint: We need to find the least common multiple of 2, 3, 6. First we need to find the common multiples of 2, 3, 6 from their multiples. Then we find the least common one among them. We can also take the simultaneous factorisation of those two numbers to find the LCM. As they are coprime numbers, we take their multiplication.

Complete step by step solution:
We need to find the LCM of 2, 3, 6. LCM stands for least common multiple.
We first find the multiples of 2, 3, 6.
The multiples of 2 are $2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,.......$.
The multiples of 3 are $3,6,9,12,15,18,21,24,27,30,.......$.
The multiples of 6 are $6,12,18,24,30,36,42,48,........$.
The least common multiple of 2, 3, 5 is 6.
We also can use the simultaneous factorisation to find the greatest common factor of 2, 3, 6.
Therefore, the least common multiple of 2, 3, 6 is 6.

Note:
We need to remember that the LCM has to be only one number. It is the least common multiple of all the given numbers. If the given numbers are prime numbers, then the LCM of those numbers will always be the multiple of those numbers. These rules follow for both integers and fractions.