Question

Question 190

A merchant has 120 L of oil of one kind, 180 L of another kind and 240 L of a third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such in tin?

Answer 1

Here, the greatest capacity of tin will be equal to the HCF of 120, 180, 240.
$\begin{array}{cc}2& 120\\ 2& 60\\ 2& 30\\ 3& 15\\ 5& 5\\ & 1\end{array}\begin{array}{cc}2& 180\\ 2& 90\\ 3& 45\\ 3& 15\\ 5& 5\\ & 1\end{array}\begin{array}{cc}2& 240\\ 2& 120\\ 2& 60\\ 2& 30\\ 3& 15\\ 5& 5\\ & 1\end{array}$
Prime factorisation of 120 $=2\times 2\times 2\times 3\times 5$
Prime factorisation of 180 $=2\times 2\times 3\times 5\times 3$
Prime factorisation of 240 $=2\times 2\times 2\times 3\times 5\times 2$
Common factors of 120, 180 and 240 are 2 (occuring twice), 3 and 5.
Thus, the HCF of 120, 180 and 240 $=2\times 2\times 3\times 5=60$
$\therefore$ Greatest capacity of tin = HCF of 120, 180 and 240 = 60 L