Identify Common Factors, Common Multiples and Prime Numbers - Reasoning

Esin is pondering a number that fits a specific set of mathematical criteria. The number in question must be a multiple of both 5 and 6, which implies that it should be divisible by the least common multiple (LCM) of these two numbers. Additionally, the number must have 100 as a factor, meaning it can be expressed as 100 multiplied by some other integer. Furthermore, Esin's number needs to be less than 1,000. The task is to determine what Esin's number could be and whether there is more than one possible option that satisfies all these conditions.

Upon analyzing the conditions, we can determine that the LCM of 5 and 6 is 30, so Esin's number must be a multiple of 30. Since it also has 100 as a factor, the number must be a multiple of 100 as well. Combining these two factors, we look for common multiples of 30 and 100 that are less than 1,000. The options that meet these criteria are 300, 600, and 900. Thus, there are indeed multiple possibilities for Esin's number, offering a range of solutions that confirms the presence of more than one option.