he manager at the local diner wants to order cups and lids. Cups come in packages of 25, and lids come in packages of 40. The manager wants to have the same number of each. What is the least number of each item the manager can order?
To find the least number of cups and lids the manager can order, we need to find the least common multiple (LCM) of 25 and 40.
The prime factorization of 25 is 5^2.
The prime factorization of 40 is 2^3 * 5.
To find the LCM, we take the highest power of each prime factor. So, the LCM of 25 and 40 is 2^3 * 5^2 = 200.
Therefore, the manager would need to order 200 cups and 200 lids in order to have the same number of each.
To determine the least number of each item the manager can order, we need to find the lowest common multiple (LCM) of 25 and 40.
Step 1: Find the prime factors of each number:
25 = 5 * 5
40 = 2 * 2 * 2 * 5
Step 2: Identify the common prime factors and include the highest exponent for each factor:
Common prime factors: 2 (highest exponent = 3), 5
LCM = 2^3 * 5 * 5 = 200
Therefore, the manager can order 200 cups and 200 lids to have an equal number of each.
To find the least number of cups and lids the manager can order, we need to find the least common multiple (LCM) of the numbers 25 and 40.
Step 1: Determine the prime factorization of each number:
- 25 = 5 * 5
- 40 = 2 * 2 * 2 * 5
Step 2: Calculate the LCM by taking the highest power of each prime factor that appears in either factorization:
- LCM = 2^3 * 5^2 = 8 * 25 = 200
Therefore, the manager should order 200 cups and 200 lids to have the same number of each item, which is the least number possible.