Question

verify
LCM × HCF =product of 2 number for the following numbers

1176 and 216
3192 and 14280​

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

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

Answer 2

Step-by-step explanation:

LCM of 1176 and 216 = 10584

HCF of 1176 and 216 = 24

Their product = 10584 × 24 = 2540416

Product of the numbers = 1176 × 216 = 254016

Here, we can say that the product of the numbers is same as their product of LCM and HCF.

Let's verify it with another example :-

LCM of 3192 and 14280 = 1899240

HCF of 3192 and 14280 = 24

Their product = 45,581,760

Product of the numbers = 3192 × 14280 = 45,581,760.

Therefore, we can say that the product of two numbers is same as the product of their HCF and LCM.

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