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.
Please mr sue give me what must be the least capacity of the bottle
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To find the least capacity of the bottle, we need to find the smallest amount of milk that can be evenly divided among all three glasses a whole number of times.
The smallest possible amount of milk that can fill all three glasses evenly is the least common multiple (LCM) of their capacities.
The capacities of the glasses are 4 liters, 6 liters, and 8 liters.
Step 1: Find the LCM of 4, 6, and 8.
- Prime factorize each number:
- 4 = 2^2
- 6 = 2 * 3
- 8 = 2^3
- Now take the highest power of each prime factor that appears in any of the numbers
=> LCM of 4, 6, and 8 = 2^3 * 3 = 24 liters.
Therefore, the least capacity of the bottle should be 24 liters to be able to fill the glasses an exact number of times.