For three consecutive natural numbers, the minimum number is a multiple of 15, the middle number is a multiple of 17, and the maximum number is a multiple of 19. What are the three natural numbers You must be right ample reward

For three consecutive natural numbers, the minimum number is a multiple of 15, the middle number is a multiple of 17, and the maximum number is a multiple of 19. What are the three natural numbers You must be right ample reward

2430243124322430 = 15 * 1622431 = 17 * 1432432 = 19 * 128 let these three numbers be X-2, X-1, XX = 19 * AX-1 = 17 * bx-2 = 15 * c19a-17b = 1 2A = 17 (B-A) + 1 19a-15c = 2 4A = 15 (C-A) + 2, that is, 2a-1 (4a-2) is a multiple of 17, 4a-2 is a multiple of 15, 2a-1 = 15 * 17 A = 128

There are three consecutive natural numbers, the smallest is a multiple of 15, the middle is a multiple of 17, and the largest is a multiple of 19

Analysis: the three numbers 15, 17 and 19 are odd, and the difference between the two adjacent numbers is 2, so their least common multiple is still an odd number. The sum of the least common multiple plus 15, 17 and 19 is even, and the difference between the two adjacent numbers is still 2. We divide the three sums by 2, and we can get a

Three consecutive natural numbers, from small to large, are multiples of 7, 11 and 13. What is the minimum sum of these three numbers?

11 / 7 = 1 + 4 / 7 = 1 + 1 / (7 / 4) = 1 + 1 / (1 + 3 / 4) = 1 + 1 / [1 + 1 / (4 / 3)] = 1 + 1 / [1 + 1 / (1 + 1 / 3)] 1 + 1 / [1 + 1 / 2 = 3 / 2 2 2 * 11-3 * 7 = 1 72 * 11-113 * 7 = 113 / 11 = 1 + 2 / 11 = 1 + 1 / (11 / 2) = 1 + 1 / (5 + 1 / 2) 1 + 1 / 6 = 7 / 6 6 6 * 13-7 * 11 = 1 61 * 13-72 * 11 = 1, the minimum number is 791