The Canadian singer's singles Sorry, Love yourself and What do you mean took first, third and fifth place. Sorry pushed Adele's Hello to second place from the top spot that it had occupied for three weeks.
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Lennon's Imagine was top, Happy Xmas (War Is Over) was third and (Just Like) Starting Over fifth in January 1981, the month after he was shot dead in New York.
Bieber's songs all come from his album Purpose which sold 90,000 copies this week. Every track from it charted inside the top 100 singles.
But it was narrowly beaten to top position in the album chart by four-piece boy band One Direction's Made in the AM which is now the fastest-selling album of 2015.
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Both Bieber's Purpose and One Direction's Made in the AM broke the record for most-streamed album in the first week of release on online streaming platform Spotify.
Purpose set a new record with 205 million global streams while Made in the AM was streamed 106 million times, both outpacing the previous record holder, The Weeknd's Beauty Behind The Madness, which garnered 90 million global streams in September.
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