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there are three heaps of rice making 120 kg 144 kg and 204 kg find the maximum capacity of a bag so that the rice of each heap can be packed in exact number of bags​

Answer :

Final answer:

The problem pertains to finding the Greatest Common Divisor (GCD) of three numbers. Using the Euclidean algorithm, we subtract the smallest number from the other two and continue this process until we reach a number that all three can be divided evenly by, which in this case is 12 kg.

Explanation:

The problem presented is finding the greatest common divisor (GCD) of three numbers: 120kg, 144kg, and 204kg.

This is a Mathematics problem pertaining to the number theory concept.

You want to find the largest bag size such that each heap of rice can be packed into an exact number of these bags.

The Greatest Common Divisor (GCD) or Highest Common Factor (HCF) is the largest number that divides exactly into a set of numbers.

In this case, we can use the Euclidean algorithm to compute the GCD.

Subtract the smallest heap size 120 kg from the other two heaps yielding two amounts: 24 kg (144-120) and 84 kg (204-120).

Next, subtract the smaller of these two numbers (24 kg) from the larger (84 kg) to get 60 kg.

Repeat this process of subtraction with 60 kg and the smaller previous amount 24 kg, to get 12 kg.

Finally, subtract 12 kg from 24 kg and from 60 kg to get multiples of 12 kg.

So the largest bag size that can be used to pack each heap in an exact number of bags is 12 kg.

Learn more about Greatest Common Divisor:

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