Relatively late mastery of scalar implicatures has been suggested to correlate with children's immature processing capacities, such as their limited working memory. Yet, many studies that tested for a link between children's working memory and their computation of scalar implicatures have failed to find any correlation. One possible reason is that the children in these studies showed little individual variation in computing scalar implicatures. The present study therefore tested for an effect of working memory in younger children, who still clearly displayed difficulties with scalar implicatures and showed greater individual variation. Subjects were 4- to 7-year-old children acquiring either English or Mandarin Chinese. A covered-box task was used to investigate the computation of scalar implicatures associated with 'some'. A digit span task was used to measure their working memory. Neither the Mandarin-speaking children nor the English-speaking children computed scalar implicatures at an adult-like level. Moreover, a significant correlation was observed between children's computation of scalar implicatures and their digit spans. These results have provided new support for a processing approach to the observed late mastery of scalar implicatures.