Question

Three jars of milk contain 40 l, 50 l, and 60 l, of milk. Find the greatest capacity of a vessel which can empty out each jar with the exact number of fillings.

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Answer 1

Explanation:

To find the greatest capacity of a vessel that can empty out each jar with the exact number of fillings, we need to find the greatest common divisor (GCD) of the three jar capacities.

So, we calculate the GCD of 40, 50, and 60.

Find the prime factors of each number:

40 = 2^3 x 5

50 = 2 x 5^2

60 = 2^2 x 3 x 5

Now, we take the highest power of each prime factor that appears in the prime factorizations of the numbers:

2^3 x 3 x 5^2

Therefore, the GCD of 40, 50, and 60 is 2^3 x 3 x 5^2.

The greatest capacity of a vessel is then 2^3 x 3 x 5^2, which is equal to 200 liters.