Question 5 - Figure it out - Page 63, 64 - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

Transcript

Question 5 A cowherd took all his cows to graze in the fields. The cows came 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 less than 200 cows, how many cows did he have? (Based on the folklore mathematics from Karnataka.)Since the cows can be divided equally into groups of 3, 5, and 7, the total number must be a multiple of the LCM of 3, 5, and 7. Finding LCM of 3, 5, 7 There are no common factors between 3, 5, 7. ∴ LCM of 3, 5, 7 = 3 × 5 × 7 = 15 × 7 = 105 Now, Number of cows is a multiple of LCM i.e. 105 Multiples of 105 are: 105, 210... The problem says he had less than 200 cows. Thus, the cowherd had 105 cows