Workers of industry A take a holiday every 5th day, while workers of industry B take a holiday every 6th day. If today workers of both indurstires were on holiday, then when next will they both be on a holiday again?

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Solution

Industry A workers take holiday on every 5th day.
Industry B workers take holiday on every 6th day.

The next time both workers will be on a holiday will be at the LCM of 5 and 6.
Multiple of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and so on.
Multiple of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54 and so on.
Least common multiple = 30,

Thus, after 30 days wokers of both the industries will be on holidays together.

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