A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres 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 a tin?
The capacity of tins should be such that it is a factor of 120, 180, and 240 so that they can be filled in tins of equal capacity.
Hence, the greatest capacity of such a tin = HCF 0f 120, 180 and 240
120 = 2 × 2 × 2 × 3 × 5
180 = 2 × 2 × 3 × 3 × 5
240 = 2 × 2 × 2 × 2 × 3 × 5
Hence, LCM = product of unique divisors = 2 × 2 × 2 × 3 × 5 × 3 × 2 = 720