A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of third kind.

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A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of 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?


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Salim Ahmed Kawsar

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Quantity of oil A = 120 liters
Quantity of oil B = 180liters
Quantity of oil C = 240liters
We want to fill oils A, B and C in tins of the same capacity

∴ The greatest capacity of the tin chat can hold oil. A, B and C = HCF of 120, 180 and 240
By fundamental theorem of arithmetic
120 = 23 × 3 × 5
180 = 22 × 32 × 5
240 = 24 × 3 × 5
HCF = 22 × 3 × 5 = 4 × 3 × 5 = 60 litres
The greatest capacity of tin = 60 litres

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Salim Ahmed Kawsar

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To find greatest capacity of tin we should find HCF of 120 and 180 and 240

Prime factors of 120 = 2 × 2 × 2 × 3 × 5

Prime factors of 180 = 2 × 2 × 3 × 3 × 5

Prime factors of 240 = 2 × 2 × 2 × 2 × 3 × 5

Therefore HCF of 120, 180 and 240 is:

2 × 2 × 3 × 5 = 60

Therefore the greatest capacity of a tin is 60 Liters

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