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If the least common multiple of two 6-digit integers has 10 digits, then their greatest common divisor has at most how many digits?

 Apr 25, 2019

please don't post questions multiple times on here. Thank you!!

 Apr 25, 2019

Here is my attempt:
The maximum LCM of two 6-digit numbers is 2 x 6=12 digits. Example:993053 x 993043=990,116,542,279(12 digits)

The minimum LCM of two 6-digit numbers is 2 x 6 -1=11 digits. Example:100213x100847=10,106,180,411(11 digits)

If their LCM is 10 digits, then that means they must share one common divisor between them. That common divisor could be a 1-digit number or a 2-digit number at a maximum.

Example:LCM{110210, 100500} = 1,107,610,500(10 digits)

                GCD {110210, 100500} =10 (2 digits)
Therefore, the GCD of the two 6-digit numbers can have at most 2 digits.

 Apr 25, 2019

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