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2015-04-26T11:29:23+05:30

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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.
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2015-04-26T21:32:37+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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.

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