Every few days a student at a school will receive a souvenir such as a pencil or shirt. Every 24th day a student receives a souvenier. Every 56th day a student receives a souveiner and every 64th day a student receives a souvenier. Which student will be the first to have all three souveniers. Show your thinking clearly and give a final statement.
(Prime factorization) I've done a quiz with this question on it and I'm almost 100% sure i got the question wrong. I wrote the answer as the GCF of the 3 numbers
Well, if you got the question wrong, there's little hope of getting the right answer.
You have not made it clear how we decide which student gets which souvenir when.
I believe you'd have to get the LCM and GCF by prime factorization to get the answer somehow? Even if you were to get the right answer your quiz is over just wait till you get it back and ask your teacher about it so you can learn from your mistake.
To solve this problem, we need to find the least common multiple (LCM) of 24, 56, and 64. The LCM represents the smallest number that is divisible by all three numbers.
To find the LCM, we can use prime factorization. Let's start by determining the prime factorization of each number:
- For 24: 2^3 x 3^1
- For 56: 2^3 x 7^1
- For 64: 2^6
Now, we need to consider the highest exponent for each prime factor. In this case, the highest exponent for the factor 2 is 6, for 3 is 1, and for 7 is 1. Therefore, the LCM is calculated as:
LCM = 2^6 x 3^1 x 7^1 = 64 x 3 x 7 = 1344
So, the first student to receive all three souvenirs will be on the 1344th day.
The GCF (greatest common factor) is not applicable in this case because we need to find the first instance where all three souvenirs are received, not the highest number that evenly divides all three numbers.