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added 10 characters in body
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Dead Possum
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Python 2, 111 9595 93 bytes

Using unpacking in replace(*'01') as in @Rod answer
-1618 bytes thanks to @Lynn

l=[1,input()]
while l[0]-l[1]cmp(*l):l[0]+=eval('*'.join(`l[0]`.replace(*'01')));l.sort()
print l[0]  

Try it online!Try it online!

Python 2, 111 95 bytes

Using unpacking in replace(*'01') as in @Rod answer
-16 bytes thanks to @Lynn

l=[1,input()]
while l[0]-l[1]:l[0]+=eval('*'.join(`l[0]`.replace(*'01')));l.sort()
print l[0]  

Try it online!

Python 2, 111 95 93 bytes

Using unpacking in replace(*'01') as in @Rod answer
-18 bytes thanks to @Lynn

l=[1,input()]
while cmp(*l):l[0]+=eval('*'.join(`l[0]`.replace(*'01')));l.sort()
print l[0]  

Try it online!

added 4 characters in body
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Dead Possum
  • 3.4k
  • 13
  • 25

Python 2, 111111 95 bytes

Using unpacking in replace(*'01') as in @Rod answer
-16 bytes thanks to @Lynn

l=[1,input()]
while l[0]-l[1]:l[0]+=eval('*'.join(`l[0]`.replace(*'01')));l=(l,l[::-1],l)[cmp;l.sort(*l)]
print l[0]  

Try it online!Try it online!

Python 2, 111 bytes

Using unpacking in replace(*'01') as in @Rod answer

l=[1,input()]
while l[0]-l[1]:l[0]+=eval('*'.join(`l[0]`.replace(*'01')));l=(l,l[::-1],l)[cmp(*l)]
print l[0]  

Try it online!

Python 2, 111 95 bytes

Using unpacking in replace(*'01') as in @Rod answer
-16 bytes thanks to @Lynn

l=[1,input()]
while l[0]-l[1]:l[0]+=eval('*'.join(`l[0]`.replace(*'01')));l.sort()
print l[0]  

Try it online!

added 122 characters in body
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Dead Possum
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  • 13
  • 25

Python 2, 113111 bytes

Using unpacking in replace(*'01') as in @Rod answer

l=[1,input()]
while l[0]-l[1]:l[0]+=eval('*'.join(`l[0]`.replace('0','1'*'01')));l=(l,l[::-1],l)[cmp(*l)]
print l[0]  

Try it online!Try it online!

Python 2, 113 bytes

l=[1,input()]
while l[0]-l[1]:l[0]+=eval('*'.join(`l[0]`.replace('0','1')));l=(l,l[::-1],l)[cmp(*l)]
print l[0]  

Try it online!

Python 2, 111 bytes

Using unpacking in replace(*'01') as in @Rod answer

l=[1,input()]
while l[0]-l[1]:l[0]+=eval('*'.join(`l[0]`.replace(*'01')));l=(l,l[::-1],l)[cmp(*l)]
print l[0]  

Try it online!

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Dead Possum
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