Consider two positive integers and which are such that is divisible by 2000. What is the least possible value of the product .
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2 0 0 0 ∣ a b b a ⇒ 2 ∣ a or b and 5 ∣ a or b . Thus, the least possible value of ab = 1 0 . Now possibilities of (a,b) = ( 1 , 1 0 ) ( 2 , 5 ) ( 5 , 2 ) ( 1 0 , 1 ) . But in all these cases 2 0 0 0 doesn’t divide a b b a . The next multiple of 1 0 is 2 0 . Now 2 0 0 0 ∣ a b b a in some cases, Answer = 2 0