Any multiple of the lcm of 170 and 253 will do as a common denominator.
The lcm(170, 253) = 43010, so the common denominator of 170 and 253 can be any of:
43010, 86020, 129030, 172040, 215050, 258060, 301070, 344080, 387090, 430100, 473110, 516120, 559130, 602140, 645150, 688160, 731170, 774180, 817190, 860200, 903210, 946220, 989230, 1032240, 1075250, 1118260, 1161270, 1204280, 1247290, 1290300, 1333310, 1376320, 1419330, 1462340, 1505350, 1548360, 1591370, 1634380, 1677390, 1720400, 1763410, 1806420, 1849430, 1892440, 1935450, 1978460, 2021470, 2064480, 2107490, 2150500, 2193510, 2236520, 2279530, 2322540, 2365550, 2408560, 2451570, 2494580, 2537590, 2580600, 2623610, 2666620, 2709630, 2752640, 2795650, 2838660, 2881670, 2924680, 2967690, 3010700, 3053710, 3096720, 3139730, 3182740, 3225750, 3268760, 3311770, 3354780, 3397790, 3440800, 3483810, 3526820, 3569830, 3612840, 3655850, 3698860, 3741870, 3784880, 3827890, 3870900, 3913910, 3956920, 3999930, 4042940, 4085950, 4128960, 4171970, 4214980, 4257990, 4301000, ...
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4/17 can be written 40/170, and 3/10 can be written as 51/170. When written that way they have (least) common denominator 170.
A few synonyms for common denominator are , common divisor, common measure, denominator, numerator
A common denominator of 20 and 30 is 600. This is NOT the least common denominator, though.
The greatest common denominator is infinite. The least common denominator is 45.
A common denominator, though not the least, is 80.