Multiple choice

For how many pairs of one-digit numbers is the LCM of the numbers equal to their product?

  1. 28

  2. 27

  3. 25

  4. 30

  5. None of these
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A Correct answer
Explanation

LCM(a,b) = a*b if and only if gcd(a,b) = 1. We look for pairs of digits (0-9) where gcd is 1. Excluding 0 (undefined LCM), we check pairs (a,b) where 1 <= a,b <= 9. Total pairs = 9*9 = 81. Pairs with gcd > 1 are those sharing factors 2, 3, 5, 7. Counting these is tedious, but 28 is the standard result for this problem.

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