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Math Help - Divisibility (gcd) 4

  1. #1
    Sea
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    Divisibility (gcd) 4

    Show that: (a,b)=(a,c)=1 \Rightarrow (a,b,c)=1
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  2. #2
    o_O
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    Let d = (a,b,c). This implies d \mid a, d \mid b, and d \mid c.

    But this means d is a common divisor of a and b. So d \mid (a,b).

    Can you finish?
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  3. #3
    Sea
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    I think...


    (a,b)=1 and (a,c)=1

    (a,b,c)=d \Rightarrow d|a ,d|b and d|c \Rightarrow d|a, d|b and d|a,d|c \Rightarrow d|(a,b) and d|(a,c)\Rightarrow d|1 \Rightarrow<br />
d=1


    \therefore (a,b)=1 and (a,c)=1   \Rightarrow (a,b,c)=1
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  4. #4
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