Question

LCM of 2/3, 8/9, 64/81, 10/27​

Answer 1

iven : Fractions \frac{2}{3}, \frac{8}{9}, \frac{64}{81},\frac{10}{27}

3

2

,

9

8

,

81

64

,

27

10

To find : The HCF of fraction ?

Solution :

The highest common factor of fractions is given by,

\text{HCF of a Fraction}=\frac{\text{HCF of the numerators of the fractions}}{\text{LCM of the Denominators of the Fractions}}HCF of a Fraction=

LCM of the Denominators of the Fractions

HCF of the numerators of the fractions

HCF of the numerator 2,8,64,10

Factors of the number is

2=2\times 12=2×1

8=2\times2\times 28=2×2×2

64=2\times2\times2\times 2\times 2\times 264=2×2×2×2×2×2

10=2\times 510=2×5

HCF(2,8,64,10)=2HCF(2,8,64,10)=2

LCM of the denominator 3,9,81,27

3 | 3 9 81 27

3 | 1 3 27 9

3 | 1 1 9 3

3 | 1 1 3 1

| 1 1 1 1

LCM(3,9,81,27)=3\times3\times 3\times 3=81LCM(3,9,81,27)=3×3×3×3=81

So, HCF of \frac{2}{3}, \frac{8}{9}, \frac{64}{81},\frac{10}{27}

3

2

,

9

8

,

81

64

,

27

10

\text{HCF}(\frac{2}{3}, \frac{8}{9}, \frac{64}{81},\frac{10}{27})=\frac{2}{81}HCF(

3

2

,

9

8

,

81

64

,

27

10

)=

81

2

Answer 2

The LCM of $\frac{2}{3} ,\frac{8}{9} ,\frac{64}{81} ,\frac{10}{27}$ is $\frac{320}{3}$

Given,

$\frac{2}{3} ,\frac{8}{9} ,\frac{64}{81} ,\frac{10}{27}$

To Find,

Find the LCM of $\frac{2}{3} ,\frac{8}{9} ,\frac{64}{81} ,\frac{10}{27}$

Solution,

• Least Common Multiple is what the abbreviation LCM stands for.
• The lowest relevant multiple of the two is the lowest number that can be divided by both. The calculation can be performed using either two or more numbers or two or more fractions.
• The LCM of two numbers can be calculated in a variety of ways.
• One of the quickest methods to find the LCM of positive numbers is to use the greatest common divisor of each number and then compute the product of the largest powers of the identical prime factors.

we know that,

LCM = lcm of (numerators)/hcf of (denominators)

so, LCM of 2,8,64 and 10 = 320

and, HCF of 3, 9,27 and 81 = 3

therefore, the LCM of $\frac{2}{3} ,\frac{8}{9} ,\frac{64}{81} ,\frac{10}{27}$ is $\frac{320}{3}$

Hence, the LCM of $\frac{2}{3} ,\frac{8}{9} ,\frac{64}{81} ,\frac{10}{27}$ is $\frac{320}{3}$

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For more information about LCM, you can refer to the following questions

How to find LCM of any number

https://brainly.in/question/4052831

How to find L.C.M. ??????

https://brainly.in/question/5636095