We present an improved determination of the Hubble constant from Hubble Space Telescope (HST) observations of 70 long-period Cepheids in the Large Magellanic Cloud (LMC). These were obtained with the same WFC3 photometric system used to measure extragalactic Cepheids in the hosts of SNe Ia. Gyroscopic control of HST was employed to reduce overheads while collecting a large sample of widely separated Cepheids. The Cepheid period-luminosity relation provides a zero-point-independent link with 0.4% precision between the new 1.2% geometric distance to the LMC from detached eclipsing binaries (DEBs) measured by Pietrzynski+ (2019Natur.567..200P) and the luminosity of SNe Ia. Measurements and analysis of the LMC Cepheids were completed prior to knowledge of the new DEB LMC distance. Combined with a refined calibration of the count-rate linearity of WFC3-IR with 0.1% precision, these three improved elements together reduce the overall uncertainty in the geometric calibration of the Cepheid distance ladder based on the LMC from 2.5% to 1.3%. Using only the LMC DEBs to calibrate the ladder, we find H_0_=74.22+/-1.82km/s/Mpc including systematic uncertainties, 3% higher than before for this particular anchor. Combining the LMC DEBs, masers in NGC 4258, and Milky Way parallaxes yields our best estimate: H_0_=74.03+/-1.42km/s/Mpc, including systematics, an uncertainty of 1.91%-15% lower than our best previous result. Removing any one of these anchors changes H0 by less than 0.7%. The difference between H0 measured locally and the value inferred from Planck CMB and {Lambda}CDM is 6.6+/-1.5km/s/Mpc or 4.4{sigma} (P=99.999% for Gaussian errors) in significance, raising the discrepancy beyond a plausible level of chance. We summarize independent tests showing that this discrepancy is not attributable to an error in any one source or measurement, increasing the odds that it results from a cosmological feature beyond {Lambda}CDM.