Question

A merchent has 120 litres of oil of 1 kind, 180 litres of another kind and 240 litres of third kind. He
wants to sell the oil by filling the 3 kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin.

Answer 1

We need a number that is the greatest common factor of 120, 180 and 240.

Start by finding gcd(120, 240) : 
240 = 120*2 + 0
Therefore the gcd of 120 and 240 is 120.

Next find gcd(120,180) :
180 = 120*1 + 60
120 = 60*2 + 0
Therefore gcd of 120 and 180 is 60

That means 60 is the greatest common factor of 120, 180 and 240.
Consequently the greatest capacity of tin is 60 litres.

Answer 2

Let M, N and P be integers.

we want to fill 120 liters in N cans of capacity V liters.
        and also fill 180 litres in  M cans of capacity V litres.
        and also fill 240 litres in P cans of capacity V litres.
    
   120 = 2 * 2 * 3 * 5 * 2 = N * V  
   180 = 2 * 2 * 3 * 5 * 3 = M * V
   240 = 2 * 2 * 3 * 5 * 4 = P * V

V is the common factor of 120 ,  180 and 240.  It can be 2 or 4 or 6 or 12 or 10 or 15 or 30 or 20 or 60.

As we want the greatest capacity of V, then  it is the greatest common divisor or factor of 120, 180 and 240.   We can see the GCD of these numbers from the above prime factors of these numbers.
  
    As GCD (120, 180, 240) = 2*2*3*5 = 60,  the answer is 60 litres.