# Is there at least one pair from $a, b, c$ that is coprime?

I have encountered a question asked by my friend, which is stated as follows:

Suppose there exists integers a, b, c, k, l, m such that $$ka+lb+mc=1$$, then, is the following statement true?

"There exists at least one pair from $$(a, b)$$, $$(b,c)$$,$$(a,c)$$ that is coprime."

Personally, I think the statement is plausible as I can assume one of k, l, and m is zero, which would mean that there exists one pair of coprime numbers. However, I have difficulty in proving it strictly. Many thanks for your help.

It is false. Example: $$10+6-15=1$$