Final answer:
To find the smallest number of avocados that can be placed in baskets with 50 and 75 pieces, calculate the least common multiple (LCM) of 50 and 75, which is 150 avocados.
Step-by-step explanation:
The smallest number of avocados that can be placed in baskets with 50 and 75 pieces can be found by calculating the least common multiple (LCM) of the two numbers. The LCM of 50 and 75 is the smallest number that is a multiple of both 50 and 75.
Factors of 50 are 1, 2, 5, 10, 25, 50.
Factors of 75 are 1, 3, 5, 15, 25, 75.
We find that 25 is the highest common factor (HCF) of 50 and 75.
To find the LCM, we use the formula:
LCM(a, b) = (a × b) / HCF(a, b)
So,
LCM(50, 75) = (50 × 75) / 25
LCM(50, 75) = 3750 / 25
LCM(50, 75) = 150
Therefore, the smallest number of avocados you can have to fill both a 50-piece basket and a 75-piece basket evenly is 150 avocados.