Find the smallest regular number that is not less than N

Question

Regular numbers are numbers that evenly divide powers of 60. As an example, 60² = 3600 = 48 × 75, so both 48 and 75 are divisors of a power of 60.

Answer 1

You want to find the smallest number m that is m >= N and m = 2^i * 3^j * 5^k where all i,j,k >= 0.

Taking logarithms the equations can be rewritten as:

 log m >= log N
 log m = i*log2 + j*log3 + k*log5

You can calculate log2, log3, log5 and logN to (enough high, depending on the size of N) accuracy. Then this problem looks like a Integer Linear programming problem and you could try to solve it using one of the known algorithms for this NP-hard problem.