Question 1 - Page 56 - Least, but not Last! - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

Transcript

Question 1 - Page 56 Do you remember the ‘Idli-Vada’ game from Grade 6 (see chapter ‘Prime Time’)? Two numbers are chosen and whenever players come to their multiples, ‘idli’ or ‘vada’ should be called out depending on whose multiple the number is. If the number happens to be a common multiple, then ‘idli-vada’ should be called out. In each problem below, the two numbers corresponding to ‘idli’ and ‘vada’ are given. Find the first number for which ‘idli-vada’ will be called out: (a) 4 and 6 (b) 7 and 11 (c) 14 and 30 (d) 15 and 55 Is the answer always the LCM of the two numbers? Explain.Idli Vada game looks like this Imagine a fun game played in a circle where children count numbers. But there's a twist! Instead of saying a multiple of 3 (like 3, 6, 9), you say "idli". Instead of saying a multiple of 5 (like 5, 10, 20), you say "vada". And for a number that's a multiple of both 3 and 5, you shout "idli-vada"! The first number for which you would say "idli-vada" is 15, as it's a multiple of both 3 and 5. These numbers that are multiples of both are called common multiples. And, the first number is the Least Common Multiple Now, let’s find Find the first number for which ‘idli-vada’ will be called out in the question (a) Game with 4 and 6 Multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60. Multiples of 6 : 6, 12, 18, 24, 30, 36, 42, 48, 54, 60. Common Multiples: 12, 24, 36, 48, 60. The first common multiple is 12 (b) Game with 7 and 11 Multiples of 7 : 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84 Multiples of 11 : 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, Common Multiples: 77, 154 The first common multiple is 77 (c) Game with 14 and 30 Multiples of 14 : 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238 Multiples of 30 : 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330 Common Multiples: 210, 420, … The first common multiple is 210 (d) Game with 15 and 55 Multiples of 15 : 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, … Multiples of 55 : 55, 110, 165, 220, 275, 330, 385, 440, 495, 550, … Common Multiples: 165, 330 The first common multiple is 165 Now, we are asked Is the answer always the LCM of the two numbers? Explain. Look at 4 and 6. LCM of 4 & 6 is 12 But, Idli-Vada game first number was 24 This is because 4 and 6 share a common factor (2). Thus, answer is not always LCM