Question

tammy must choose a number between 67 and 113 what is a multiple of 4, 6, and 8? what are all the numbers she could choose?

Answer 1

Since
`x` is simultaneously a multiple of 4, 6, and 8, it must be also be a multiple of the least common multiple of the three, which would be 24. So any
`x=24n`, where
`n` is an integer, such that
`67\le x\le113` will belong to the desired set of numbers.

The number of positive multiples of 24 less than or equal to 113 is
`\left\lfloor(113)/(24)\right\rfloor=4`, while the number of positive multiples of 24 less than or equal to 67 is
`\left\lfloor(67)/(24)\right\rfloor=2`, so there are
`4-2=2` numbers that are each multiples of 4, 6, and 8, and fall between 67 and 113. These numbers are 72 and 96.