Multiple Surprises Ishan

I solved these problems by first finding a starting number for each sequence and noticing a pattern. For the first challenge (multiples of 2, 3, 4), I found that the sequence 14, 15, 16 works. I noticed that you can keep finding new sequences by adding 12 to the first number each time, giving sets like 26, 27, 28 and 38, 39, 40. 12 is the LCM of 2, 3, and 4. I could use the following formula to find sequences of consecutive numbers that are multiples of other numbers: First Number of Sequence = (Your First Found Number) + (LCM × k), where k is any whole number. For example, for consecutive numbers that are multiples of 3, 4 and 5, you can automatically find one sequence (3, 4, 5), and and the LCM of 3, 4 and 5 is 60. Using the formula, we can subsitute the numbers to make 'n = 3 + 12k'. Then, we can find multiple sequences if we swap out 'k' for other numbers such as 1 to get 15, 16, 17 or 2 to get 27, 28, 29. I used this method to find patterns for 4 and 5 consecutive sets. For the last question, I found the highest power of each prime to get 2520. Then, I used the LCM and the first number (1) to get the formula n = 1 + 2520k. Then I could find the next set of consecutive numbers that follow this rule and they are k = 1 → 2521, 2522, 2523, 2524, 2525, 2526, 2527, 2528, 2529, 2530.