Printable

2018 AMC 10B Problem 23

Include the solution Back to the problem

2018 AMC 10B Problem 23AMC 10 Step by Step

Name: Date: September 13, 2026

GCD & LCM · difficulty 4 of 5 · about 7 min · position P21-25

How many ordered pairs $(a, b)$ of positive integers satisfy the equation $a\cdot b + 63 = 20\cdot \text{lcm}(a, b) + 12\cdot\text{gcd}(a,b),$ where $\text{gcd}(a,b)$ denotes the greatest common divisor of $a$ and $b$ , and $\text{lcm}(a,b)$ denotes their least common multiple?

A)
$\text{ 0}$
B)
$\text{ 2}$
C)
$\text{ 4}$
D)
$\text{ 6}$
E)
$\text{ 8}$

2018 AMC 10B Problem 23

Working