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?

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

Answer: 18 baskets.

Step-by-step 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.