Question

How do you find the LCM of 20, 24?

Answer 1

Hint: We need to find the LCM of 20, 24. First we need to find the multiple of 20 and 24. The multiples can be found by multiplying natural numbers with those numbers. Then we find the lowest common multiple of those two numbers. The first multiple that is common for both of them will be their LCM. 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, 24. LCM stands for lowest common multiple.
We first find the multiples separately for 20 and 24.
We are going to multiply the natural numbers with those numbers to find their multiples.
The multiples of 20 are $20,40,60,80,100,120,140,......$.
The multiples of 24 are $24,48,72,96,120,144,......$.
The first common multiple of 20 and 24 is 120. There is no lower number than 120 which can be a common multiple for both 20 and 24.
We also can use the simultaneous factorisation to find the lowest common multiple of 20 and 24.
We have to divide both of them with possible primes which can divide both of them.
\[\begin{align}
  & 2\left| \!{\underline {\,
  20,24 \,}} \right. \\
 & 2\left| \!{\underline {\,
  10,12 \,}} \right. \\
 & 1\left| \!{\underline {\,
  5,6 \,}} \right. \\
\end{align}\]
The only possible number that divides both of them is $2\times 2=4$. Therefore, the lowest common multiple of 20 and 24 is $4\times 5\times 6=120$.

Note: We need to remember that the LCM has to be only one number. It is the lowest possible 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.