What is the smallest number of avocados that can be placed in baskets with 50 and 75 pieces
150, I guess.
To determine the smallest number of avocados that can be placed in baskets with 50 and 75 pieces, we need to find the greatest common divisor (GCD) of 50 and 75.
One way to find the GCD is by using the Euclidean algorithm, which involves repeatedly dividing the larger number by the smaller number until the remainder is zero. The last non-zero remainder is the GCD.
Let's follow the steps:
1. Divide 75 by 50: 75 ÷ 50 = 1 with a remainder of 25.
2. Divide 50 by 25: 50 ÷ 25 = 2 with no remainder.
3. The remainder is zero, so the GCD is the last non-zero remainder, which is 25.
Therefore, the smallest number of avocados that can be placed in baskets with 50 and 75 pieces is 25.
To find the smallest number of avocados that can be placed in baskets with 50 and 75 pieces, we need to find the least common multiple (LCM) of 50 and 75.
Step 1: Write down the prime factorization of each number:
- The prime factorization of 50 is 2 * 5^2.
- The prime factorization of 75 is 3 * 5^2.
Step 2: Identify the common prime factors and take the highest exponent for each factor:
- Both 50 and 75 have a common prime factor of 5^2.
Step 3: Multiply the common prime factors with the highest exponents and any remaining prime factors:
- LCM = 2 * 3 * 5^2 = 2 * 3 * 25 = 150.
Therefore, the smallest number of avocados that can be placed in baskets with 50 and 75 pieces is 150.