Question

LCM of two numbers is 15 times of their HCF.if the product of the numbers is 14415. Find the HCF

Answer 1

Let HCF be x

LCM=15x

HCF *LCM=product of two no.

15x²=14415

x²=961

x=31

Answer 2

Answer:

The value of HCF = 31.

Step-by-step explanation:

Given:

LCM of two numbers is 15 times their HCF

If the product of the numbers is 14415.

To find:

the value of HCF

Step 1

Let the numbers are a and b

then, HCF = x and LCM = 15x

We know that HC F $\times$ LCM = a $\times$ b

x (15x) = 14415

15$x^{2}$ = 14415

$x^{2} = \frac{14415}{15}$

= 961

$x^{2}=961$

Step 2

For $x^{2}=f(a)$ the solutions exists $x=\sqrt{f(a)},-\sqrt{f(a)}$

$x=\sqrt{961}, x=-\sqrt{961}$

$\sqrt{961}=31$

$-\sqrt{961}=-31$

x = 31, x = -31

Therefore, the value of HCF = x = 31.

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