Question

The two numbers are in the ratios 2:3 and their LCM 72 HCF of a reminder is...

Answer 1

The HCF is the highest common factor of 2x and 3x i.e. x. Now we know that, The numbers are 24 and 36. Therefore, the HCF is 12.

Answer 2

AnswEr

☯ Given Ratio of both numbers is 2 : 3.

And, their LCM is 72.

We've to find out the HCF of both numbers.

Let's consider that numbers are 2x & 3x. And, HCF be x.

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⠀⠀By Using Formula :

$\star\ \boxed{\sf{\pink{ Product \ of \ two \ numbers \ = \ HCF \times LCM}}}$

Substituting, values in the Given Formula:

$:\implies\sf 2x \times 3x = x \times 72 \qquad \bigg\lgroup\sf LCM \: = \: 72 \bigg\rgroup\\\\\\:\implies\sf 6x^2 = 72 x \\\\\\:\implies\sf x = \dfrac{\cancel{72}}{\cancel{\: 6}}\\\\\\:\implies\boxed{\frak{\purple{x = 12}}}$

$\therefore\underline{\textsf{ Hence, HCF of Both the numbers is \textbf{12}}}.$

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$\qquad\qquad{\underline{\underline{\bigstar \: \bf\:Some \ More \ Information \ :}}}$⠀

• HCF (Highest Common factor) which is the largest factor of the given numbers.

• LCM (Least Common Factor) which can be easily divided by the lowest present number.