Did I solve this problem right? Here is the question: Use least common multiple or greatest common factor to solve this problem. Mark has 153 hot dogs and 261 hot dog buns. He wants to put the same number of hot dogs and hot dog buns on each tray. What is the greatest number of trays that Mark can use to accomplish this? My answer is 9 because I used the greatest common factor. Is this correct? Thanks.
yes
Try both and see which one you think makes more sense
To determine if your answer is correct, let's solve this problem step by step using both the least common multiple (LCM) and the greatest common factor (GCF) methods.
First, let's find the GCF of 153 and 261. The GCF is the largest number that divides both 153 and 261 evenly. To find the GCF, we can either list the factors of both numbers or use prime factorization.
The prime factorization of 153 is 3 x 3 x 17 (where 3 and 17 are prime).
The prime factorization of 261 is 3 x 3 x 29 (where 3 and 29 are prime).
To find the GCF, we take the common factors and multiply them together: 3 x 3 = 9. So, the GCF of 153 and 261 is 9.
Next, let's find the LCM of 153 and 261. The LCM is the smallest multiple that both 153 and 261 divide into evenly. We can find the LCM using the prime factorization method.
The prime factorization of 153 is 3 x 3 x 17.
The prime factorization of 261 is 3 x 3 x 29.
To find the LCM, we take the least number of times each prime factor appears: 3 (from 153) x 3 (from 261) x 17 (from 153) x 29 (from 261) = 41649. So, the LCM of 153 and 261 is 41649.
Now, to determine the greatest number of trays Mark can use, we divide the common factor (GCF) by the number of buns per tray. In this case, the GCF is 9. If Mark puts 9 buns on each tray, he must also put 9 hot dogs on each tray to balance the number of buns and hot dogs per tray.
Therefore, the correct answer is 9 trays, which means your answer is indeed correct. Well done!