Answer to Question #250612 in Discrete Mathematics for Alina

Question

Let a and b be two Natural Numbers, such that the greatest common divisor of a and b is 63, and the least common multiple of a and b is 44452800. If ’b’ is an odd number, what is the minimum value of ’a’ possible? [Hint: a · b = gcd(a, b) · lcm(a, b)]

Answer 1

$\gcd{(a,b)}=63\\ lcm {(a,b)}=44452800\\ ab=\gcd{(a,b)} \times lcm {(a,b)}=63\times 44452800=2800526400$

Since $b$ is odd, then $a$ is odd.

Since their gcd is 63, then they are both multiples of 63.

The minimum value of a is 63.