Answer to Question #21680 in Combinatorics | Number Theory for sarita

Question

there are 48 pepsi bottles,84 mirinda bottles and 60 sprite bottles in a shop. these bottles are to be put in crate, so that each crate has the same number of bottles with same cold drink.find the greatest number of bottles in each crate

Answer 1

Greatest number of bottles in each crate is the same as greatest common divisor of number of each type of cold drink.
So,
The divisors of 48 are: 1, 2, 3, 4, 6, 8, 12, 24, 48.
The divisors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 42, 84.
The divisors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
The numbers that these tree lists share in common are the common divisors of 48, 84 and 60:
1, 2, 3, 4, 6, 12.
The greatest of these is 12.
GCD(48, 84, 60) = 12
Answer: 12.