Question

Three containers contain 27 litres, 36 litres, 72 litres of milk. What biggest measure can measure exactly the milk in the three containers?

Answer 1

Hint: We need to find the biggest measure that can measure exactly the milk in the three containers. We are trying to find the greatest common divisor of 27, 36, 72. We apply the process to find g.c.d of those numbers and find the solution of the problem.

Complete step by step answer:
Three containers contain 27 litres, 36 litres, 72 litres of milk. We need to find the biggest measure that can measure exactly the milk in the three containers.
The biggest possible measurement is a mug of x litres.
This means x can fully divide all three volumes of the container of 27 litres, 36 litres, 72 litres.
X becomes the common divisor of 27, 36, 72.
We need to find the greatest possible value for x which means x has to be the greatest common divisor of 27, 36, 72.
We find the g.c.d of those numbers.
$\begin{align}
  & 3\left| \!{\underline {\,
  27,36,72 \,}} \right. \\
 & 3\left| \!{\underline {\,
  9,12,24 \,}} \right. \\
 & 1\left| \!{\underline {\,
  3,4,8 \,}} \right. \\
\end{align}$
We can see that the greatest possible divisor will be $3\times 3=9$.
9 divides all three of them.

Therefore, the biggest measure that can measure exactly the milk in the three containers is 9.

Note: We can also find the number of times we have to measure using the 9-litre pot. The last possible quotients are that number. So, we have to measure 3, 4, 8 times to measure them respectively.