Question

Find the hcf&lcf of Each the following pairs of integers and verify that lcm×hcf=product of two numbers a130,364 b850,276 c90,144

Answer 1

Answer:

Question 2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. 26 and 91 (ii) 510 and 92 (iii) 336 and 54

Question 2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

26 and 91 (ii) 510 and 92 (iii) 336 and 54

Answer:

(i)

26 = 2 x 13

91 =7 x 13

HCF = 13

LCM =2 x 7 x 13 =182

Product of two value 26 x 91 = 2366

Product of HCF and LCM 13 x 182 = 2366

Hence, product of two numbers = product of HCF × LCM

(ii)

510 = 2 x 3 x 5 x 17

92 =2 x 2 x 23

HCF =2

LCM =2 x 2 x3 x 5 x 17 x 23 = 23460

Product of both values 510x92 = 46920

Product of HCF and LCM 2x23460 =46920

Hence, product of two numbers = product of HCF × LCM

(iii)

336 = 2 x 2 x 2 x 2 x 3 x 7

54 = 2 x 3 x 3 x 3

HCF = 2 x 3 = 6

LCM = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 =3024

Product of number 336 x 54 =18144

Product of HCF and LCM 6 x 3024 = 18144

Hence, product of two numbers = product of HCF × LCM

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