We present a new observational study of the ^ { 12 } CO ( 1–0 ) line emission as an H _ { 2 } gas mass tracer under extreme conditions in extragalactic environments . Our approach is to study the full neutral interstellar medium ( H _ { 2 } , H i and dust ) of two galaxies whose bulk interstellar medium ( ISM ) resides in environments that mark ( and bracket ) the excitation extremes of the ISM conditions found in infrared luminous galaxies , the starburst NGC 3310 and the quiescent spiral NGC 157 . Our study maintains a robust statistical notion of the so-called X = N ( { { H _ { 2 } } } ) / I _ { CO } factor ( i.e . a large ensemble of clouds is involved ) while exploring its dependency on the very different average ISM conditions prevailing within these two systems . These are constrained by fully-sampled ^ { 12 } CO ( 3–2 ) and ^ { 12 } CO ( 1–0 ) observations , at a matched beam resolution of Half Power Beam Width \sim 15 ^ { \prime \prime } , obtained with the James Clerk Maxwell Telescope ( JCMT ) on Mauna Kea ( Hawaii ) and the 45-m telescope of the Nobeyama Radio Observatory ( NRO ) in Japan , combined with sensitive 850 \mu m and 450 \mu m dust emission and H i interferometric images which allow a complete view of all the neutral ISM components . Complementary ^ { 12 } CO ( 2–1 ) observations were obtained with JCMT towards the center of the two galaxies . We found an X factor varying by a factor of 5 within the spiral galaxy NGC 157 and about 2 times lower than the Galactic value in NGC 3310 . In addition , the dust emission spectrum in NGC 3310 shows a pronounced submm “ excess ” . We tried to fit this excess by a cold dust component but very low temperatures were required ( T _ { C } \sim 5 - 11 K ) with a correspondingly low gas-to-dust mass ratio of \sim 5 - 43 . We furthermore show that it is not possible to maintain the large quantities of dust required at these low temperatures in this starburst galaxy . Instead , we conclude that the dust properties need to be different from Galactic dust in order to fit the submm “ excess ” . We show that the dust SED can be fitted by an enhanced abundance of Very Small Grains ( VSGs ) and discuss different alternatives .