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Question A cowherd took all his cows to graze in the fields. The cows can go to a crossing with 3 gates. An equal number of cows passed through each gate. Later, at another crossing with 5 gates again an equal number of cows passed through each gate. The same happened at the third crossing with 7 gates. If the cowherd had fewer than 200 cows, how many cows did he have? (Based on the folklore mathematics from Karnataka).
No. of cows is divisible by 3, 5, 7. This means the number of cows is a multiple of the LCM(3, 5, 7). The total number of cows is also less than 200. LCM (3, 5, 7) = 3 × 5 × 7 = 105 No. of cows must be a multiple of 105. Multiples of 105 are 105, 210, 315. The problem states that the cowherd had fewer than 200 cows. Only multiples of 105 that are less than 200 are 105. Hence cowherd had 105 cows.