Question

What is the lowest common multiple of $5,7$ and $10$ ?

Answer 1

Hint: Here we have to find the lowest common multiple of the given three numbers. We will find the lowest common multiple of the three numbers by using the prime factor method. We will find the prime factor of all the given numbers and then multiply the prime factors with the highest exponent power among them. Finally the product we get is our desired answer.

Complete step-by-step answer:
We have to find the lowest common multiple of the given numbers:
$5,7$ And $10$
Firstly we will find the prime factor of each numbers as follows:
We know $5$ and $7$ are prime numbers so we can write them as:
$5=1\times 5$….$\left( 1 \right)$
$7=1\times 7$….$\left( 2 \right)$
Next we will calculate the prime factor of $10$ by using long division method as follows:
$\begin{align}
  & 2\left| \!{\underline {\,
  10 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5 \,}} \right. \\
 & \,\,\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$
So we get,
$10=1\times 2\times 5$….$\left( 3 \right)$
From equation (1), (2), (3) we have the highest exponent power of $1,2,5,7$ as $1$ so,
LCM $\left( 5,7,10 \right)=1\times 2\times 5\times 7$
LCM $\left( 5,7,10 \right)=70$
So we get the LCM for $70$ .
Hence the lowest common multiple of $5,7$ and $10$ is $70$ .
So, the correct answer is “70”.

Note: LCM known as lowest common multiple is the smallest common multiple of two or more numbers such that it is the least common multiple which is completely divided by all the numbers given. We can find the LCM of the numbers by writing down the multiple of all the numbers given and finding the lowest common multiple among them but that method becomes complicated when the numbers given are big. Prime factorization method is simple and mostly used where we divide the number by the prime numbers starting with $2$ till we get the remainder as $1$ .