The GCD of two numbers is 4 and their LCM is 400 how many pairs of values can be numbers assume

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Since the GCD is 4, the two numbers are of the form 4x and 4y, where x and y are coprime. Since x and y are coprime, their LCM is 4xy.

Therefore, we need to find all pairs of coprime numbers that satisfy xy=100. Going over all options (not that many), we get that x and y can be either (1,100) or (4,25). The original numbers are therefore either (4,400) or (16,100).

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