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The managers of franks snack shack buys hamburgers in packages of 30 and hamburger buns in packages of 24. He cannot buy part of a pack. What is the least number of packages of each product that he can by to have an equal number of hamburgers buns? How many of each will he have?

Respuesta :

Answer:

He has to buy 4 packages of hamburgers in packages of 30 and 5 packages of hamburgers in packages of 24

Step-by-step explanation:

First we have to calculate the least common multiple (LCM) of 24 and 30

We will calculate the LCM of 24 and 30 by prime factorization method

24 = 2*2*2*3 = [tex]2^{3} * 3^{1}[/tex]

30 = 2*3*5 = [tex]2^{1} *3^{1}* 5^{1}[/tex]

LCM = [tex]2^{3}* 3^{1}*5^{1}[/tex]

LCM = 120

So number of hamburger buns = 120

Therefore, he must buy 120/24 = 5 packages of hamburgers in packages of 24 and he must also buy 120/30 = 4 packages of hamburgers in packages of 30

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