A bottle contains some milk. Three glasses of capacity 4l,6l,and 8l are to be filled an exact number of times from it. What must be the least capacity of the bottle.
Perhaps I am missing something, but if we fill each of the labeled bottles just once, the big bottle can contain as little as 18 L
1 x (4L + 6L + 8L) = 18L
To find the least capacity of the bottle, we need to consider the requirements for filling each glass an exact number of times. Let's analyze the different possibilities.
First, let's start by examining the smallest glass, which has a capacity of 4 liters.
To fill this glass an exact number of times, the bottle's capacity must be a multiple of 4 liters. This means the least capacity of the bottle should be at least 4 liters.
Next, let's consider the glass with a capacity of 6 liters.
To fill this glass an exact number of times, the bottle's capacity must be a multiple of 6 liters. This means the least capacity of the bottle should be at least 6 liters.
Finally, let's consider the glass with a capacity of 8 liters.
To fill this glass an exact number of times, the bottle's capacity must be a multiple of 8 liters. This means the least capacity of the bottle should be at least 8 liters.
To satisfy all three requirements, the least common multiple (LCM) of 4, 6, and 8 must be determined.
The LCM of 4, 6, and 8 is 24, meaning that the least capacity of the bottle should be at least 24 liters to ensure that each glass can be filled an exact number of times.
Thus, the minimum capacity of the bottle should be 24 liters.