Kevin makes snack bags that each contain a box of raisins and a granola bar. each package of raisins contains 9 boxes. the granola bars come 12 to a package. what is the least number he can buy of each so he has exactly the same number of each. how many packages of each should he buy?

Given : Kevin makes snack bags that each contain a box of raisins and a granola bar. Each package of raisins contains 9 boxes. The granola bars come 12 to a package.

Now,

The least number he can buy of each so he has exactly the same number of each will be :-

Number of raisins bag he should buy =

Number of granola bars package he should buy =

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

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