Question 1 (Page 116) - Co-prime numbers (and art) - Chapter 5 Class 6 - Prime Time (Ganita Prakash)

Transcript

Question 1 (Page 116) While playing the ‘idli-vada’ game with different number pairs, Anshu observed something interesting! Sometimes the first common multiple was the same as the product of the two numbers. At other times the first common multiple was less than the product of the two numbers. Find examples for each of the above. How is it related to the number pair being co-prime? This is our idli vada game. We notice that For numbers 3 & 5 We say ‘idli-vada’ at Number 15 Which is multiplication of both numbers i.e. 3 × 5 = 15 This, is because numbers 3 & 5 have only 1 as common factor So, since 3 & 5 are co-prime – we say ‘idli-vada’ at their multiplication Now, let’s check other pairs For numbers 4 & 6 We say ‘idli-vada’ at Number 12 Which is less than multiplication of both numbers i.e. 4 × 6 = 24 This, is because numbers 4 & 6 has common factor 1, 2 Since there is more than one common factor, thus numbers are not co-prime So, since numbers are not co-prime – we say ‘idli-vada’ at less than their multiplication For numbers 3 & 7 We say ‘idli-vada’ at Number 21 Which is multiplication of both numbers i.e. 3 × 7 = 21 This, is because numbers 3 & 7 have only 1 as common factor So, since 3 & 7 are co-prime – we say ‘idli-vada’ at their multiplication The Relationship with Co-prime Numbers The relationship Anshu observed is as follows: When a pair of numbers is co-prime, their first common multiple is equal to their product. When a pair of numbers is not co-prime, their first common multiple is less than their product.