Question

the hcf of two numbers is 6 and lcm of the same numbers is 72. lf one number is 18, find the other number.​

Answer 1

Answer:

answer for the given problem is given

Answer 2

$\huge\sf\pink{Answer}$

☞ Other Number is 24

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$\huge\sf\blue{Given}$

✭ HCF = 6

✭ LCM = 72

✭ One Number = 18

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$\huge\sf\gray{To \:Find}$

◈ The other Number?

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$\huge\sf\purple{Steps}$

Let the other number be x

We know that,

$\small\underline{\boxed{\sf Product \ of \ Numbers = HCF \times LCM}}$

Substituting the given values,

➳ $\sf 18\times x = 6 \times 72$

➳ $\sf 18x = 432$

➳ $\sf x=\dfrac{432}{18}$

➳ $\sf \orange{x =24}$

Verification

➝ $\sf 18 =2\times 3\times 3$

➝ $\sf 24 = 2\times 2\times2\times3$

LCM is the product of the largest power of all the factors

➢ $\sf 2^3\times 3^2$

➢ $\sf LCM = 72$

HCF is the product of the least power of the common factors

➢ $\sf 2\times 3$

➢ $\sf HCF = 6$

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