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Two numbers are coprime when their greatest common divisor is 1, meaning they share no prime factor. Euclid's algorithm computes the gcd by repeated remainder, and coprimality is exactly the condition for a modular inverse to exist.
Coprimality
gcd(a, b) = 1
Product identity
gcd(a, b) × lcm(a, b) = a × b
Yes. 35 = 5 × 7 and 64 = 2⁶ share nothing, so the gcd is 1 and the lcm is 2240.
No. 8 and 9 are both composite yet coprime.