Q1.
Which is the first number for which the players should say, ‘idli-vada’? It is 15, which is a multiple of 3, and also a multiple of 5. Find out other such numbers that are multiples of both 3 and 5. These numbers are called _____________________________.
Answer
The players say ‘idli-vada’ exactly at the numbers that are in the 3 table and in the 5 table.
Multiples of 3 → 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, …
Multiples of 5 → 5, 10, 15, 20, 25, 30, 35, 40, 45, …
Multiples of 5 → 5, 10, 15, 20, 25, 30, 35, 40, 45, …
The numbers that appear in both lists are
15, 30, 45, 60, 75, 90, 105, 120, …
These are exactly the numbers in the 15 table. So the blank is filled as:
These numbers are called common multiples of 3 and 5.
Why they are the multiples of 15: a number that is a multiple of 3 and of 5 must contain both a 3 and a 5 as factors, so it must be a multiple of 3 × 5 = 15. That is why every 15th number in the game is an ‘idli-vada’ number.
Tip: to find the common multiples of any two numbers quickly, write the table of the bigger one and tick the numbers that the smaller one also divides.