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Extracurricular activities

Extracurricular activities

In my institute they organize five extracurricular activities in the afternoon: Sports, literature, photography, chess and singing. The sport activity is celebrated one day yes and another no; that of literature once every three days; that of photography every four days; the one of chess every five days and the one of song one of every six. On January 1, all the activities coincided on the same day and then each one continued with its periodicity.

Can you tell me how many afternoons in the first quarter did all extracurriculars agree?

Solution

Simply find the least common multiple of 2, 3, 4, 5 and 6 (which is 60). We know therefore that they will meet again on the 61st day of the year and that therefore the third match will already be in the second quarter, after 120 days. The answer is therefore 2 (On March 1 and 2-3, depending on whether the year was leap or not)