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

Question #21680
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
1
Expert's answer
2013-01-10T08:19:49-0500
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.

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