Question

A dentist is making identical dental care bags for patients using 56 tubes of toothpaste, 112 packets of floss, and 85 toothbrushes. What is the greatest number of identical dental care bags the dentist can make with the least amount of items leftover. Describe the contents of each bag.

Answer 1

Greatest number of identical dental care bags is equal to the L.C.M. of 56, 112 & 85.

56 = 2 x 2 x 2 x 7
112 = 2 x 2 x 2 x 2 x 7
85 = 5 x 17

L.C.M. (56, 112, 85) = 2 x 2 x 2 x 2 x 5 x 7 x 17
= 560 x 17
= 9520

Therefore, 9520 is the correct answer.

Answer 2

If we leftover 1 toothbrush, we will have:
56 tubes of toothpaste, 112 packets of floss and 84 toothbrushes.
The greatest common factor:
GCF ( 56, 112, 84 ) = 28
56 : 28 = 2, 112 : 28 = 4, 84 : 28 = 3
Answer:
The greatest number of identical dental care bags is 28.
In every bag will be 2 tubes of toothpaste, 4 packets of floss and 3 toothbrushes. One toothbrush will be leftover.