+0  
 
-1
42
1
avatar

Suppose a and b are positive integers such that the units digit of a is 2, the units digit of b is 4, and the greatest common divisor of a and b is 8. What is the smallest possible value of the least common multiple of a and b?

 May 20, 2022
 #1
avatar+9457 
0

Note that \(\operatorname{lcm}(a, b) = \dfrac{ab}{\gcd(a, b)}\), so if we want the smallest value of lcm, we want to minimize the product a * b.

 

That means a and b must be as small as possible.

 

The smallest number with unit digit 2 and divisible by 8 is 32.

The smallest number with unit digit 4 and divisible by 8 is 24.

 

Can you continue from here?

 May 20, 2022

14 Online Users