Prime Time | A

Question 1

Let us now play the 'idli-vada' game with different pairs of numbers:

(a) 2 and 5, (b) 3 and 7, (c) 4 and 6.

We will say 'idli' for multiples of the smaller number, 'vada' for multiples of the larger number and 'idli-vada' for common multiples. Draw a figure similar to Fig. 5.1 if the game is played up to 60.

Solution

Understand the Question

In this game, numbers up to $60$ $60$ are checked for multiples of two given numbers:
- 'Idli': Multiples of the smaller number.
- 'Vada': Multiples of the larger number.
- 'Idli-vada': Common multiples of both numbers.
To find the 'idli-vada' numbers, list all multiples of each number up to $60$ and find the numbers common to both lists.

(a) 2 and 5

Step 1 · Find Multiples and Common Multiples of 2 and 5

Diagram 1

Multiples of $2$ ('idli') up to $60$ : $2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60$

Multiples of $5$ ('vada') up to $60$ : $5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60$

Common multiples ('idli-vada'): $10, 20, 30, 40, 50, 60$

Answer

(a) $10, 20, 30, 40, 50, 60$

(b) 3 and 7

Step 1 · Find Multiples and Common Multiples of 3 and 7

Diagram 2

Multiples of $3$ ('idli') up to $60$ : $3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60$

Multiples of $7$ ('vada') up to $60$ : $7, 14, 21, 28, 35, 42, 49, 56$

Common multiples ('idli-vada'): $21, 42$

Answer

(b) $21, 42$

(c) 4 and 6

Step 1 · Find Multiples and Common Multiples of 4 and 6

Diagram 3

Multiples of $4$ ('idli') up to $60$ : $4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60$

Multiples of $6$ ('vada') up to $60$ : $6, 12, 18, 24, 30, 36, 42, 48, 54, 60$

Common multiples ('idli-vada'): $12, 24, 36, 48, 60$

Answer

(c) $12, 24, 36, 48, 60$

Common Mistakes

Stopping Short of 60: Forgetting to include $60$ when it is a multiple (e.g. for $2$ , $5$ , $4$ , and $6$ ).
Multiplying the Numbers for Common Multiples: Assuming common multiples of $4$ and $6$ are only multiples of $4 \times 6 = 24$ , missing intermediate common multiples like $12, 36, 60$ .

Question 1

More questions in A

Co-prime art

A prime puzzle

Rules