Question

The product of two number is 864.If their LCM.is 72,what is there H.C.F.​

Answer 1

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➡️Let the HCF be x.

So, HCF × LCM = Product of numbers. =

Or, x × 72 = 864

Or, x = 864/72 = 12.

➡️Hence, their HCF is 12.

That's it..

$\textbf{Hope\: it\: helps\: you\: ❤️ }$

Answer 2

Concept

The greatest number that totally divides two numbers is known as the Highest Common Factor (HCF). The Greatest Common Divisor (GCD) is another name for the Highest Common Factor (HCF).

The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.

The relationship between any two numbers, a and b, and their Highest Common Factor (HCF) and Least Common Multiple (LCM) is stated as:

$\[a\times b=HCF\left( a,b \right)\times LCM\left( a,b \right)\]$

Given

The Least Common Multiple (LCM) of the two numbers is $72$ and the product of the two numbers is $864$.

Find

We have to find the Highest Common Factor (HCF) of the two numbers.

Solution

Consider the two numbers be $\[a\text{ }and\text{ }b\]$, then

$\[a\times b=864\]$

The value of Least Common Multiple (LCM) is $72$, i.e.

$\[LCM\left( a,b \right)=72\]$

Now, using $\[a\times b=HCF\left( a,b \right)\times LCM\left( a,b \right)\]$, we get

$\[864=HCF\left( a,b \right)\times 72\]$

$\[HCF\left( a,b \right)=\frac{864}{72}\]$

$\[HCF\left( a,b \right)=12\]$

Hence, $12$ is the required Highest Common Factor (HCF) of the two numbers.

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