Modular Multiplicative inverse of exact multiples

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How to calculate the inverse of $23$ with respect to mod 138. I am having difficulty because $138$ is an exact multiple of $138$. If anybody could help me.

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It doesn't have an inverse because it's a divisor of 138. If your modulus is $n$, then $a$ will have an inverse if and only if $(a,n)=1$.