17. The sum of two integers $A$ and $B$ is 2010 . If the lowest common multiple of $A$ and $B$ is 14807 , write down the larger of the two integers $A$ or $B$.
17. Ans: 1139 .
A direct way to solve the problem is to factor 14807 directly. Alternatively, one may hope for $A$ and $B$ to have common factors to simplify the problem. This is a good strategy because of the following fact:
"The greatest common divisor of $A$ and $B$, equals the greatest common divisor of $A+B$ and $\operatorname{lcm}(A, B)$."
2010 is easily factored as $2 \times 3 \times 5 \times 67$. Checking that 67 is also a factor of 14807 , we can conclude that 67 is also a factor of $A$ and $B$. The problem is reduced to finding $a$ and $b$ such that
$$
a+b=\frac{2010}{67}=30 \quad \text { and } \quad a b=\frac{14807}{67}=221 .
$$

Since 221 can be factoredeasily, $a$ and $b$ must be 13 and 17 . So the answer is $17 \times 67=1139$.