Question

What is the least common multiple of 20, 15 and 8?

Answer 1

Hint: We need to find the least common multiple of 20, 15 and 8. First we need to find the common multiples of 20, 15 and 8 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.

Complete step by step answer:
We need to find the LCM of 20, 15 and 8. LCM stands for least common multiple.
We first find the multiples of 20, 15 and 8.
The multiples of 20 are $20,40,60,80,100,120,140,160,....$.
The multiples of 15 are $15,30,45,60,75,90,105,120,135,150,....$.
The multiples of 8 are $8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,........$.
The least common multiple of 20, 15 and 8 is 120.
We also can use the simultaneous factorisation to find the greatest common factor of 20, 15 and 8.
We have to divide both of them with possible primes which can divide both of them.
\[\begin{align}
  & 2\left| \!{\underline {\,
  8,15,20 \,}} \right. \\
 & 2\left| \!{\underline {\,
  4,15,10 \,}} \right. \\
 & 5\left| \!{\underline {\,
  2,15,5 \,}} \right. \\
 & 1\left| \!{\underline {\,
  2,3,1 \,}} \right. \\
\end{align}\]
The LCM is $2\times 2\times 2\times 3\times 5=120$.
Therefore, the least common multiple of 20, 15 and 8 is 120.

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.