Question

lcm of 1/3,5/6,5/9,10/27

Answer 1

$\bf \red{LCM \left(\frac{1}{3}, \: \frac{5}{6}, \: \frac{5}{9}, \: \frac{10}{27} \right) = \frac{10}{3} }$

Given:

• $\frac{1}{3}, \: \frac{5}{6}, \: \frac{5}{9} , \: \frac{10}{27}$

To find:

• Find the LCM.

Solution:

Concept to be used:

LCM of fractions: $\frac{\bf LCM \: of \: numerators}{\bf HCF \: of \: denominators}$

Step 1:

Find LCM of numerators.

Numerators of fractions are 1,5,5,10.

$5 = 5 \times 1 \\ 5 = 5 \times 1 \\ 10 = 2 \times 5 \times 1$

$LCM(1,5,5,10)= 5 \times 2$

or

$\bf LCM(1,5,5,10) = 10$

Step 2:

Find HCF of denominators.

Denominators of fractions are 3,6,9,27.

$3 = 3 \times 1 \\ 6 = 2\times 3 \times 1 \\ 9 = 3 \times 3 \times 1 \\ 27 = 3 \times 3 \times 3 \times 1$

$\bf HCF(3,6,9,27) = 3$

Step 3:

Find LCM of fractions.

$LCM \left(\frac{1}{3}, \: \frac{5}{6}, \: \frac{5}{9}, \: \frac{10}{27} \right) = \frac{LCM(1,5,5,10}{HCF(3,6,9,27)}$

or

$LCM \left(\frac{1}{3}, \: \frac{5}{6}, \: \frac{5}{9}, \: \frac{10}{27} \right) = \frac{10}{3}$

Thus,

$\bf LCM \left(\frac{1}{3}, \: \frac{5}{6}, \: \frac{5}{9}, \: \frac{10}{27} \right) = \frac{10}{3}$

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Learn more:

1) find the LCM of 7/2, 9/4 and 5/3

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2) what is the HCF of 2/3,3/4,4/5

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Answer 2

The answer is, (LCM)$\left(\frac{1}{3}, \frac{5}{6}, \frac{5}{9}, \frac{10}{27}\right)=\frac{10}{3}$

What is LCM and HCF?

• The full form of LCM in Maths is Least Common Multiple, whereas the full form of HCF is the Highest Common Factor.
• The H.C.F. defines the greatest factor present in between given two or more numbers, whereas L.C.M. defines the least number which is exactly divisible by two or more numbers.

According to the question:

Given:

$\frac{1}{3}, \frac{5}{6}, \frac{5}{9}, \frac{10}{27}$

Concept to be used:

LCM of fractions: $\frac{\text { LCM of numerators }}{\text { HCF of demominators }}$

Step 1:

Find LCM of numerators.

Numerators of fractions are 1,5,5,10.

$\begin{aligned}&5=5 \times 1 \\&5=5 \times 1 \\&10=2 \times 5 \times 1\end{aligned}$

(LCM)(1,5,5,10)=5 $\times$2

Or

(LCM)(1,5,5,10)=10

Step 2:

Find HCF of denominators.

Denominators of fractions are 3,6,9,27.

$3=3 \times 1\\ 6=2 \times 3 \times 1\\ 9=3 \times 3 \times 1\\ 27=3 \times 3 \times 3 \times 1$

(HCF)(3,6,9,27) = 3

Step 3:

Find LCM of fractions.

$\left(\frac{1}{3}, \frac{5}{6}, \frac{5}{9}, \frac{10}{27}\right)=$ $\frac{{LCM}(1,5,5,10}{H C F(3,6,9,27)}$

or

(LCM)$\left(\frac{1}{3}, \frac{5}{6}, \frac{5}{9}, \frac{10}{27}\right)=\frac{10}{3}$

Hence, (LCM)$\left(\frac{1}{3}, \frac{5}{6}, \frac{5}{9}, \frac{10}{27}\right)=\frac{10}{3}$

Learn more about LCM and HCF here,

https://brainly.in/question/15273412?msp_poc_exp=5

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