Prime Divisor Problem

Homework Statement

I have to prove the following:
Let a1,a2, ...,an be integers and set b=a1*a2*...*an. If c is a nonzero integer and c is relatively prime to each ak, then c and b are relatively prime.

Homework Equations

Definition of relatively prime: Let a and b be integers, not both zero. if gcd(a,b)=1 then a and b are relatively prime.

The Attempt at a Solution

1. Let a1,a2, ...,an be integers and let b=a1*a2*...*an. Suppose there exists a nonzero integer c where c is relatively prime to each ak.

2. By defn, gcd(c,ak)=1

I need help showing that the gcd(c,a1*a2)=1

Thanks

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