Manshi goes to dance class once in every 6 days, karate class once in every 12 days and art class once in every 18 days.

If she last attended all the three classes on $1^{st}$ of April, when will she next attend them together?

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Solution

To find when Manshi will next attend the the classes together, we need to find the least common multiple (LCM) of 6, 12 and 18.

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Multiples of 18 = 18, 36, 54, 72, 90, ...

36 is the least common multiple of 6, 12 and 18.

Hence, if she attended all three classes on $1^{st}$ of April, then she will next attend them after 36 days.

i.e., 36 days after $1^{st}$ of April = $7^{th}$ of May

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Manshi goes to dance class once in every 6 days, karate class once in every 12 days and art class once in every 18 days. If she last attended all the three classes on 1st of April, when will she next attend them together?

Manshi goes to dance class once in every 6 days, karate class once in every 12 days and art class once in every 18 days.

If she last attended all the three classes on $1^{st}$ of April, when will she next attend them together?