Final answer:
The smallest number of each type of towel that Josiah Linens could have sold, given they sell hand towels in sets of 12 and bath towels in sets of 3, is 12 hand towels and 12 bath towels, with the Least Common Multiple being 12.
Step-by-step explanation:
The question asks to find the smallest number of each type of towel that Josiah Linens could have sold, given that they sell hand towels in sets of 12 and bath towels in sets of 3, and the same number of each type was sold this morning.
To solve this, we need to find the Least Common Multiple (LCM) of the two numbers, which is the smallest number that is a multiple of both numbers. The LCM of 12 and 3 is 12 because 12 is the smallest number that both 3 and 12 can divide into without leaving a remainder. This means that the store could have sold 12 sets of hand towels and 4 sets of bath towels (because 12 divided by 3 equals 4), which equates to 12 hand towels and 12 bath towels in total, assuming that a set of bath towels contains exactly 3 towels.