I agree with Nikolay Z.
Other solution, with just basic math is this:
you know that the number you're looking for is a multiple of 1440. So the smallest number you are actually looking for is 1440. So let's break down 1440 (which is really easy even tough it's a big number). We know 1440 is divisible by 10 and 144 is a 12 squared. Which leave us with 12x12x10 = 3x4x3x4x2x5. So let's think that through - 10 is a multiple of 5 so we know that n>=5. We need to find the integers less than 5 that are multiples of 1440. we Have 2, 3 and 4, so we are left with 3 and 4(3x4x3x4x2x5). So the smallest multiple of 3 (remember n>=5) is 6. 8 is the smallest for 4 (that leaves us with an integer).
So the answer is 8.
Excuse me if my idea is not presented clear enough.
