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We have mapped the W3 GMC ($\sim$1.5 square degrees) in the $^{12}$CO(1-0) and $^{13}$CO(1-0) lines with the FCRAO 14-m telescope. Gas column densities and masses were derived from line ratios of the two isotopes. We then used images from the Infrared Sky Survey Atlas (ISSA) to remove the background emission from the Galactic plane, extracting the far-infrared (7 - 135 $\mu$m) luminosity from the W3 GMC itself. By comparing both the millimeter-line and IRAS continuum data, we can determine the ratio of far-infrared luminosity to molecular gas mass, L$_{\rm{IRAS}}$/M$_{\rm{CO}}$, which is often used as a measure of star formation efficiency. On scales of $\sim$1.5$^\prime$, the bulk of the cloud mass is relatively inactive (L$_{\rm{IRAS}}$/M$_{\rm{CO}}$ $\sim$2), while 3$\%$ of the total mass, confined to the most massive cores, has L$_{\rm{IRAS}}$/M$_{\rm{CO}}$ ~ 70, and contributes nearly a quarter of the total luminosity of the entire W3 GMC. Such a wide range of L$_{\rm{IRAS}}$/M$_{\rm{CO}}$ values implies that the spatially-averaged values previously determined by studies of ensembles of molecular clouds may reveal little about the character of individual star forming cores.
