Jenny goes to dance class every 6 days, karate class every 12 days, and the library every 18 days. On December 1st she went to both classes and the library. On what day will she do both classes and go to the library?
Answers
Question :- Jenny goes to dance class every 6 days, karate class every 12 days, and the library every 18 days. On December 1st she went to both classes and the library. On what day will she do both classes and go to the library ?
Solution :-
we have given that,
→ Dance class is = in Every 6 days.
→ Karate class is = in Every 12 days.
→ Library class is = in Every 18 days.
So, all three class will be on the same day on the LCM of all given days..
we have to find the LCM .
Prime factors of 6, 12 and 18 are :-
→ 6 = 2 * 3
→ 12 = 2 * 2 * 3
→ 18 = 2 * 3 * 3
LCM = 2 * 2 * 3 * 3 = 36 days.
Therefore, on every 36 days she will do all three class.
Now, we have given that, On December 1st she went to both classes and the library .
Hence,
→ She will go to all class again now = 1 Dec. + 36 days. = (1 Dec + 30 Days of Dec. ) + 6 days of Jan. = 6 January . (Ans.)
∴ On 6th January will she do both classes and go to the library.
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