99, 198, 297, 396, 495, 594, 693, 792 +99 . . .
55, 110, 165, 220, 275, 330, 385, 440, 495, 550, 605, . . .33, 66, 99, 132, 165, 198, 231, 264, 297, 330, 363, . . .44, 88, 132, 176, 220, 264, 308, 352, 396, 440, 484, . . .
The multiples of 99 are infinite. They start with these and go on forever by continuously adding 99: 99, 198, 297, 396, 495, 594, 693 +99 . . .
178 267 356 445 534
80 is divisible by: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
The Least Common Multiple (LCM) for 396 495 is 1,980.
99, 198, 297, 396, 495.
99, 198, 297, 396, 495.
99, 198, 297, 396, 495, 594, 693, 792 +99 . . .
198, 297, 396, 495, 594
99 198 297 396 495 594 693 792 891 990
All the multiples of 99, starting with these: 99, 198, 297, 396, 495, 594, 693, 792 +99 . . .
The first seven multiples of 99: 99, 198, 297, 396, 495, 594, 693
99, 198, 297, 396, 495, 594, 693, 792, 891, 990, 1089, 1188, . . .
There are 27: 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 363, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 484, 495.
Well, well, well, looks like we have a math problem on our hands. The number of positive integers that divide 2004 to leave a remainder of 24 is the same as the number of positive integers that divide 1980. Why? Because 2004 - 24 = 1980. So, the answer is the number of divisors of 1980, which can be calculated by prime factorizing 1980 and using the formula for the number of divisors. Voila!
55, 110, 165, 220, 275, 330, 385, 440, 495, 550, 605, . . .33, 66, 99, 132, 165, 198, 231, 264, 297, 330, 363, . . .44, 88, 132, 176, 220, 264, 308, 352, 396, 440, 484, . . .