Common multiples

In your book, Maths Mela (Chapter 13, Animal Jumps), a rabbit and a frog start at 0 on a number line. The rabbit jumps 4 each time: it lands on 4, 8, 12, 16, 20, 24 … The frog jumps 3 each time: it lands on 3, 6, 9, 12, 15, 18, 21, 24 … The numbers they both land on are called the common multiples of 3 and 4.

12 is the first number both animals touch, so 12 is the first common multiple of 3 and 4. They meet again at 24, then 36, then 48. Notice that each common multiple is a multiple of 12.

You can also find common multiples without a number line, by writing both times tables. Multiples of 4: 4, 8, 12, 16, 20, 24 … Multiples of 6: 6, 12, 18, 24 … The numbers in both lists, 12 and 24, are common multiples of 4 and 6. The next ones are 36 and 48.

Sometimes it is quicker. A spider jumps 3 each time and a grasshopper jumps 6. Every place the grasshopper lands (6, 12, 18 …) is also a place the spider lands, so the common multiples of 3 and 6 are 6, 12, 18, 24, 30 …