Question

Ravi said, “HCF (a, b, c) · LCM (a, b, c) = a × b × c”. Do you agree ? Justify.​

Answer 1

Answer.

No, it is only true for two numbers.

Answer Keys.

First things first, we have to write numbers as a product.

Let's define the three numbers rigorously. Assume they have HCF of k.

Three numbers are $\mathrm{a=kx, b=ky, c=kz}$, where $\mathrm{HCF(x,y,z)=1}$.

Then,

• $\mathrm{HCF(a,b,c)=k}$
• $\mathrm{LCM(a,b,c)=kxyz}$
• $\mathrm{abc=k^3xyz}$

$\therefore \boxed{\mathrm{HCF(a,b,c)\cdot LCM(a,b,c)=\dfrac{abc}{k} }}$

The equation that Ravi said doesn't hold for k≠1. So, the equation that Ravi told is not true.

More information.

The product of HCF and LCM of two numbers is the product of two numbers.

Answer 2

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NO IS THE ANSWER, BECAUSE THIS FORMULA IS ONLY FOR TWO NUMBERS...

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Assuming three numbers a, b, and c are 1, 2 and 3

PROVE

HCF (a,b,c) X LCM (a,b,c) = aXbXc

SOLUTION

HCF (1,2,3) = 1

LCM (1,2,3) = 1 X 2 X 3 = 6

SO,

HCF (1,2,3) X LCM (1,2,3)

➣ (1) X (1X2X3) = 1X2X3

HENCE,

HCF (a,b,c) X LCM (a,b,c)

❥ a X b X c

➖➖➖➖➖➖➖➖➖➖➖➖➖➖

HOPE IT HELPS