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Results of a study of the variability of the blazar J0721+7120 carried out on the RATAN-600 based on daily observations from March 5, 2010 to April 30, 2010 at five frequencies from 2.3 to 21.7 GHz are reported. In the same time interval, 13 observing sessions at 37 GHz were carried out on the 14-m radio telescope of the Metsähovi Radio Astronomy Observatory of the Aalto University School of Technology (Finland). From March 19, 2010 to October 20, 2010, 16 daily sessions at 6.2 cm and five sessions at 3.5 cm were conducted on the 32-m radio telescope of the Zelenchukskaya Observatory (Quasar-KVO complex of the Institute of Applied Astronomy, Russian Academy of Sciences). A powerful flare was detected during the observations, with a time scale of approximately 20 days, derived from an analysis of the light curves and the structure and autocorrelation functions. The flare spectrum has been determined. In five sessions on the 32-m Zelenchukskaya telescope at 6.2 cm, intraday variability with time scales 8-16 h was detected; in four sessions, trends with time scales longer than a day were observed. In three sessions at 3.5 cm, intraday variability with a time scale of approximately 5 h was detected. [ABSTRACT FROM AUTHOR]