Question

if three buckets of capacities 15 litre,18 litre and 24 litre can fill a drum in exact number of times, find the least capacity of the drum.

Answer 1

There are two questions to be solved, therefore, I'll solve the buckets one first and then I'll solve the other one. To solve both we need to apply LCM (least common multiple).

There are three buckets with differente capacities, one with 15 litres, one with 18 litres and one with 24 litres. Since they can fill a drum in an exact number of times, this means that the capacity of the drum is a multiple of the capacity of each bucket, therefore we should break each number into their multiples and find the common ones as shown below.

`\begin{gathered} 15\text{ = 3}\cdot5 \\ 18\text{ = 2}\cdot3\cdot3 \\ 24\text{ = 2}\cdot2\cdot2\cdot3 \end{gathered}`

We now need to multiply all the common multiples:

`\text{least capacity = 2}\cdot2\cdot2\cdot3\cdot3\cdot5\text{ = }360\text{ litres}`

For the second problem we have three items a book, a pen and a box. They cost respectively 36, 45 and 54. We need to then find the smallest sum of money that could buy a exact number o each item. We need to apply LCM once again as shown below:

`\begin{gathered} 36\text{ = 2}\cdot2\cdot3\cdot3 \\ 45\text{ = 3}\cdot3\cdot5 \\ 54\text{ = 2}\cdot3\cdot3\cdot3 \end{gathered}`

We now need to multiply all the common multiples:

`\text{least sum of money = 2}\cdot2\cdot3\cdot3\cdot3\cdot5\text{ = }540`