2000 AMC 12 Problem 1

Problem 1 of 25EasierAlgebra Number Theory

In the year

2001,

the United States will host the International Mathematical Olympiad. Let

I,

M,

and

O

be distinct positive integers such that the product

I \cdot M \cdot O = 2001.

What is the largest possible value of the sum

I + M + O?

Show solution

Solution

Factoring gives

2001 = 3 \cdot 23 \cdot 29.

To maximize the sum of three distinct positive integers with this product, take

I = 1,

M = 3,

and

O = 23 \cdot 29 = 667.

The largest sum is

1 + 3 + 667 = 671.

Thus, the correct answer is E.