If the HCF and LCM of two positive integers a and b are x and y respectively, then $\frac{x^{2} y^{2}}{a^{2} b^{2}}$ = _______.

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Solution

Product of two numbers = LCM × HCF
⇒ a × b = y × x
⇒ ab = xy ...(1)

Now,
$\frac{x^{2} y^{2}}{a^{2} b^{2}} = \frac{{(x y)}^{2}}{{(a b)}^{2}} = \frac{{(a b)}^{2}}{{(a b)}^{2}} (From (1)) = 1$

Hence, $\frac{x^{2} y^{2}}{a^{2} b^{2}}$ = 1 .

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If the HCF and LCM of two positive integers a and b are x and y respectively, then x2y2a2b2 = _______.

Product of two numbers = LCM × HCF ⇒ a × b = y × x ⇒ ab = xy ...(1) Now, x2y2a2b2=xy2ab2 =ab2ab2 From (1) =1 Hence, x2y2a2b2 = 1 .

If the HCF and LCM of two positive integers a and b are x and y respectively, then $\frac{x^{2} y^{2}}{a^{2} b^{2}}$ = _______.

Product of two numbers = LCM × HCF
⇒ a × b = y × x
⇒ ab = xy ...(1)

Now,
$\frac{x^{2} y^{2}}{a^{2} b^{2}} = \frac{{(x y)}^{2}}{{(a b)}^{2}} = \frac{{(a b)}^{2}}{{(a b)}^{2}} (From (1)) = 1$

Hence, $\frac{x^{2} y^{2}}{a^{2} b^{2}}$ = 1 .