n : 99 = x rest 51 => n = 99x + 51 | + 48
n : 77 = y rest 29 => n = 77y + 29 | + 48
=> n + 48 = 99 × ( x + 1)
=> n + 48 = 77 × (y + 1)
99 = 3^2 × 11
77 = 7 × 11
___________
cmmmc = 3^2 × 7 × 11 = 693
n + 48 = 693
n = 694 - 48
n = 645
________
645 : 99 = 6 rest 52
645 : 77 = 8 rest 29