Using digital roots (adding all the digits in a number up until you get a single digit) we can see that:
105: 1+0+5 = 6
63: 6+3 = 9
If both digital roots equal 3,6,and/or 9 then the LCM is always 3.
The Normal Way:
A few Multiples of 105:
105 / 5 = 21
21 / 7 = 3
3,5,7,21,105
A few Multiples of 63:
63 / 3 = 21
21 / 7 = 3
3,7,21,63
So as you can see, the LCM is 3.
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