For another picnic you want to make hamburgers with pickles, again without having any left over. You need to balance the number of packages of buns (which usually contain 8 buns) with the number of packages of hamburger patties (which usually contain 12 patties) and the number of jars of pickles (which contain 18 slices). Assume that each hamburger needs three pickle slices. What is the smallest number of packages of buns, packages of patties, and jars of pickles, respectively? Express your answer as three integers separated by commas.

you need three packs of buns, two packs of patties and four jars of pickles.

3:2:4

Will 3 pkg buns, 1 pkg hamburger patties, 2 jars pickles do it?

To determine the smallest number of packages of buns, packages of patties, and jars of pickles needed, we need to find the least common multiple (LCM) of 8, 12, and 18.

Step 1: List the prime factors of each number.
- Prime factors of 8: 2 x 2 x 2
- Prime factors of 12: 2 x 2 x 3
- Prime factors of 18: 2 x 3 x 3

Step 2: Find the maximum exponent for each prime factor.
- For the prime factor 2, the maximum exponent is 3.
- For the prime factor 3, the maximum exponent is 2.

Step 3: Multiply the prime factors raised to their maximum exponents.
2^3 x 3^2 = 8 x 9 = 72

Therefore, the smallest number of packages of buns, packages of patties, and jars of pickles needed is 72 each.