Romesh wants to make a giant balloon display using an equal number of red, white and blue balloons. What is the smallest number of packs of each colour he needs to use in order to have no balloons left over?
In order to have no balloons left over, Romesh needs to have the same number of red, white, and blue balloons. Let's denote this number as x.
Since Romesh wants to use the smallest number of packs, he needs to find the least common multiple (LCM) of the number of balloons in each pack.
Let's assume the number of red balloons in one pack is r, the number of white balloons in one pack is w, and the number of blue balloons in one pack is b.
The multiple of x, r, w, and b that is the smallest will determine the smallest number of packs Romesh needs for each color. The LCM of x, r, w, and b can be calculated as LCM(LCM(x, r), LCM(w, b)).
For example, if Romesh wants to make a display of 10 balloons and the packs contain 3, 4, and 5 balloons each, the LCM(10, 3, 4, 5) would be 60. In this case, Romesh would need to use 6 packs of each color (6 * 3 = 18 red balloons, 6 * 4 = 24 white balloons, and 6 * 5 = 30 blue balloons) in order to have no balloons left over.
To find the smallest number of packs of each color, Romesh needs to determine the LCM of x, r, w, and b based on the actual numbers he has available.