Question

A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of the 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 a tin? [4 MARKS]

Answer 1

Concept: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

The greatest capacity of a tin is the HCF of 120, 180 and 240 liters.
The prime factorisation of the given numbers is :
120=2$\times$2$\times$2$\times$3$\times$5
180=2$\times$2$\times$3$\times$3$\times$5
240=2$\times$2$\times$2$\times$2$\times$3$\times$5
Hence the highest common factor of 120,180,240=2$\times$2$\times$3$\times$5
$\because$ Highest common factor of 120, 180 and 240 is 60.
$\therefore$ Required HCF = 60 litres.
$\therefore$ Greatest capacity of a tin = 60 litres.