Rohnda is in charge of buying food for the school picnic, she found that hot dogs are in packages of 24, buns in packages of 18, ketchup in boxes of 12, and mustard in boxes of 15. what is the least number of students that can be feed if each student receives 1 of each item and there are none left over?
This is just like finding the LCM of
24, 18 ,12, and 15
24 = 2x2x2x3
18 =2x3x3
12 = 2x2x3
15 = 3x5
The LCM = 2x2x2x3x5 = 120
thanks Reiny
To determine the least number of students that can be fed if each student receives one of each item without any leftovers, we need to find the least common multiple (LCM) of the quantities 24, 18, 12, and 15.
Here's how you can calculate the LCM step by step:
1. List the prime factors of each number:
- 24: 2 * 2 * 2 * 3
- 18: 2 * 3 * 3
- 12: 2 * 2 * 3
- 15: 3 * 5
2. Identify the highest power of each prime factor from all the lists:
- 2^3 (since it appears in 24 and 12)
- 3^2 (since it appears in 24, 18, and 12)
- 5^1 (since it appears in 15)
3. Multiply the highest powers of the prime factors:
2^3 * 3^2 * 5^1 = 8 * 9 * 5 = 360
Therefore, the least number of students that can be fed with no leftovers is 360.