Complete the following table: First number ( a ) Second number ( b ) HCF Are they co-prime? LCM a × b HCF × LCM (i) 16 28 - - - - - (ii) 64 - 32 - 192 - - (iii) 15 29 - - - - -

Co-primes: Two numbers are said to be coprimes, if their HCF is 1 . We know that, the product of LCM and HCF of two numbers is equal to the product of the given two numbers. (i) First number a = 16 , Second number b = 28 Prime factorisation of 16 = 2 × 2 × 2 × 2 Prime factorisation of 28 = 2 × 2 × 7 HCF of 16 and 28 = 2 × 2 = 4 LCM of 16 and 28 = 2 × 2 × 2 × 2 × 7 = 112 HCF × LCM = 4 × 112 = 448 a × b = 16 × 28 = 448 16 and 28 are not co-primes because HCF is 4 . (ii) First number a = 64 , HCF = 28 , LCM = 192 ⇒ a × b = HCF × LCM ⇒ 64 × b = 32 × 192 ⇒ b = 32 × 192 64 = 96 HCF × LCM = 32 × 192 = 6144 a × b = 64 × 96 = 6144 64 and 96 are not co-primes beacuse HCF is 32 . (iii) First number a = 15 , Second number b = 29 Prime factorisation of 15 = 3 × 5 × 1 Prime factorisation of 29 = 29 × 1 HCF of 15 and 29 = 1 LCM of 15 and 29 = 3 × 5 × 29 = 435 HCF × LCM = 1 × 435 = 435 a × b = 15 × 29 = 435 15 and 29 are co-primes because HCF is 1 . First number Second number (b) HCF Are they co-prime? LCM a × b HCF × LCM (i) 16 28 4 No 112 448 448 (ii) 64 96 32 No 192 6144 6144 (iii) 15 29 1 Yes 435 435 435