sam was buying hot dogs and hot dog buns for a backyard barbeque.hot dogs come in packs of 16 but buns come in packs of 12. how many packs of each will sam have to buy so that there are no hot dogs or buns left over?

16 = 4*4

12 =4*3
so
4*4*3 is LCM
= 48 of each
3 packs HD
4 packs buns

To determine how many packs of hot dogs and hot dog buns Sam needs to buy, we can find the least common multiple (LCM) of 16 and 12, as the LCM will give us the minimum quantity of each item needed to ensure none are left over.

To find the LCM of 16 and 12, we can list the multiples of each number until we find a common multiple:

Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, ...

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...

From the list above, we can see that the least common multiple (LCM) of 16 and 12 is 48. This means that Sam should buy hot dogs and buns in packs of 48 to ensure none are left over.

Now, let's calculate the number of packs Sam needs to buy:

Number of packs of hot dogs = LCM of 16 and 12 divided by the quantity of hot dogs per pack
= 48 ÷ 16
= 3 packs

Number of packs of hot dog buns = LCM of 16 and 12 divided by the quantity of buns per pack
= 48 ÷ 12
= 4 packs

Therefore, Sam needs to buy 3 packs of hot dogs and 4 packs of hot dog buns to have no leftovers at the backyard barbeque.