Common multiple problems

In your book, Maths Mela (Chapter 13, Animal Jumps), there is food at the end of a cobbled road. The stones are numbered from 0 to 64, and the food is at 64. Robby the rabbit jumps 4 stones each time. Deeku the deer jumps 6 stones each time. Both start at 0. Will each of them land exactly on 64?

Robby lands on the multiples of 4: 4, 8, 12 … 60, 64. Since 4 × 16 = 64, 64 is a multiple of 4, and Robby lands right on the food. Deeku lands on the multiples of 6: 6, 12, 18 … 54, 60, and then 66. 6 × 10 = 60 and 6 × 11 = 66, so 64 is not a multiple of 6. Deeku jumps from 60 straight past 64 and never lands on it.

Common multiples also tell us when two repeating things happen together. In the book, Sher Khan the tiger goes hunting every 3rd day, and Bagheera the panther every 5th day. Counting the days from when they start, Sher Khan hunts on days 3, 6, 9, 12, 15, 18 … and Bagheera on days 5, 10, 15, 20 …

They hunt together on the days that are in both lists: the common multiples of 3 and 5. The first is day 15, then day 30, then day 45, and so on every 15 days.