Question

A grocery store is making fruit baskets using 144 apples, 108 oranges, and 90 pears . Each basket will be identical. What is the greatest number of fruit baskets the boys can make using all the fruit?

Answer 1

You can make 18 fruit baskets with 8 apples, 6 oranges, and 5 pears in each

Answer 2

Answer: 18 baskets.

Explanation:

Here we want to find the greatest common multiple of these 3 numbers, and the greatest common multiple will be the maximum number of baskets:

To find it, we took the smaller number of the set, in this case 90, and we divide it by the smaller number that we can:

90/2 = 45

now we mus see if 45 divides 144 and 108, and is easy to see that is not the case, so this is not a common factor.

Now we try with 90/3 = 30

now, 30 divides the other two numbers? of course not (the multiples of 30 are 60, 90, 120, 150, etc)

Try with the next one,

90/4 is not integer

90/5 = 18

let's see if 18 divides the other two:

108/18 = 6

144/18 = 8

So 18 is the greatest common factor, this means that we will have 18 baskets, with 8 apples, 6 oranges and 5 pears each.