Question

Find the LCM of 25 and 40 by the prime factorisation method.

Answer 1

Hint: We need to find the least common multiple of 25 and 40. First we need to find the common multiples of 40 and 25 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 25 and 40. LCM stands for least common multiple.
We first find the multiples of 40 and 25.
The multiples of 40 are $40,80,120,160,200,240,280,.......$.
The multiples of 25 are $25,50,75,100,125,150,175,200,225,250,275,........$.
The least common multiple of 40 and 25 is 200.
We also can use the simultaneous factorisation to find the greatest common factor of 40 and 25.
We have to divide both of them with possible primes which can divide both of them.
\[\begin{align}
  & 5\left| \!{\underline {\,
  25,40 \,}} \right. \\
 & 1\left| \!{\underline {\,
  5,8 \,}} \right. \\
\end{align}\]
The LCM is $5\times 5\times 8=200$.

Therefore, the least common multiple of 40 and 25 is 200.

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.