What is the absolute value of the difference of numbers whose sum is 35 and the least common multiple of 42?

The LCM must be the product of all factors into which each of the numbers can be expanded. Let us factor 42, and compose two products that would satisfy the given condition:
42 = 2 * 3 * 7.
The choice is small: 2 * 3 = 6, 2 * 7 = 14, 3 * 7 = 21. Obviously, these numbers will be 14 and 21: 14 + 21 = 35.
The difference of two numbers, taken in any order, in absolute value will be equal to 7: | 14 – 21 | = | 21 – 14 | = 7.
Answer: 7.