Common multiples

In your book, Maths Mela (Chapter 9), the frog jumps in 3s and the squirrel in 4s, both starting from 0. Some numbers are touched by both of them: 12, 24, 36 and so on. These are common multiples of 3 and 4: they are in the 3 times table AND in the 4 times table.

The rabbit jumps in 6s and the kangaroo in 8s. Both touch 24 and 48. These are common multiples of 6 and 8. A number like 16 is touched by the kangaroo but not the rabbit, and 30 by the rabbit but not the kangaroo.

Now a chase! If the cat and the rat land on the same number, the cat catches the rat. The cat is on 6 and the rat is on 12. Each time the cat jumps 3 steps forward, the rat jumps 2 steps forward at the same time. After 1 jump each: cat 9, rat 14. After 2: cat 12, rat 16. After 3: cat 15, rat 18. After 4: cat 18, rat 20. After 5: cat 21, rat 22. After 6: cat 24, rat 24. Caught!

Careful: the cat and the rat both touch 18, but not at the same time. The rat is on 18 after 3 jumps, and by the time the cat reaches 18 (after 4 jumps), the rat has moved on to 20. The cat catches the rat on 24, after 6 jumps each.