Three cans contain 12L, 16L and 24L of milk. A mug used to measure the milk in three cans such that it measure the milk exact number of times from each can. What is the maximum capacity of the mug?
Given :
Three cans contain 12L, 16L and 24L of milk. A mug used to measure the milk in three cans such that it measure the milk exact number of times from each can.
To find :
We have to find the maximum capacity of the mug.
Solution :
The highest common factor of 12, 16, 24 is the maximum capacity of the mug.
Prime factorization of $12 = 2 \times 2 \times 3$
Prime factorization of $16 = 2 \times 2 \times 2 \times 2$
Prime factorization of $24 = 2 \times 2 \times 2 \times 3$
Therefore,
HCF of 12, 16 and 24$= 2\times2 = 4$
Therefore, the maximum capacity of the mug is 4L.
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