For positive integers a & b, how many ordered pairs (a, b) are there, such that lcm of a & b is 1000?
a) 64
b) 49
c) 36
d) 25
Ans: b)49
1000 = 2353. So a = 2A5R, b = 2B5S, and max(A, b) = 3, max(R, S) = 3 (A, b) can be (0, 3), (1, 3), (2, 3), (3, 3), (3, 2), (3, 1), (3, 0). Thus there are 7 ways of choosing A, b. similarly 7 ways of choosing (R2S2). Hence 7.7 = 49 ways.