Question

1] What is the smallest number that when divided by 35, 56, 91 leaves a remainder 7 in each case?

2] Determine the number nearest to 110000 but greater than 100000 which is exactly divisible by each of 8, 15 and 21.

3] A circular field has a circumfrence of 360 km. Three cyclists start together and can cycle 48 km, 60 km and 72 km a day, round the field. When will they meet again?

Answer 1

1] The number which is exactly divisible by 8, 15 and 21 
2] above photo
3] Cyclist 1: Covers the entire circumference of field in 360/48 = 7.5 days = 180 hours
Cyclist 2: Covers the entire circumference of field in 360/60 = 6 days = 144 hours 
Cyclist 3: Covers the entire circumference of field in 360/72 = 5 days = 120 hours LCM of 180, 144, 120 gives when they would meet LCM = 720 hours = 720/ 24 = 30 days