The LCM of two numbers is 360, and the gcd is 18. Find the first number if the second is 90.

1. The product of the greatest common divisor and the least common multiple of two numbers a and b is equal to the product of the numbers themselves:

Gcd (a, b) * gcd (a, b) = ab. (1)

2. Equation (1) allows finding one number by the values of the LCM and GCD, if another is known:

GCD (a, b) = 18;
LCM (a, b) = 360;
b = 90;
a = GCD (a, b) * LCM (a, b) / b = 360 * 18/90 = 4 * 18 = 72.
Answer: 72.