The HCF and LCM of two numbers are 21 and 84 | vedclass

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(C) Given: $HCF = 21$ and $LCM = 84$.Let the two numbers be $21x$ and $21y$,where $x$ and $y$ are coprime.The ratio of the numbers is given as $1:4$,s

Vedclass · Accepted Answer

$84$

Vedclass · Answer

(C) Given: $HCF = 21$ and $LCM = 84$.Let the two numbers be $21x$ and $21y$,where $x$ and $y$ are coprime.The ratio of the numbers is given as $1:4$,so $\frac{21x}{21y} = \frac{1}{4}$,which implies $\frac{x}{y} = \frac{1}{4}$.We know the property: Product of two numbers $= HCF 	imes LCM$.So,$(21x) 	imes (21y) = 21 	imes 84$.$441(xy) = 1764$.$xy = \frac{1764}{441} = 4$.Since $\frac{x}{y} = \frac{1}{4}$,we have $y = 4x$. Substituting this into $xy = 4$,we get $x(4x) = 4$,so $4x^2 = 4$,which means $x^2 = 1$,so $x = 1$.Then $y = 4(1) = 4$.The numbers are $21(1) = 21$ and $21(4) = 84$.The larger number is $84$.

The $HCF$ and $LCM$ of two numbers are $21$ and $84$ respectively. If the ratio of the two numbers is $1:4$,then the larger of the two numbers is

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