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What is the HCF of 23,34\frac{2}{3},\frac{3}{4}32​,43​, and 56\frac{5}{6}65​​?
Question

What is the HCF of 23,34\frac{2}{3},\frac{3}{4}, and 56\frac{5}{6}​?

A.

172\frac{1}{72}​​

B.

524\frac{5}{24}​​

C.

112\frac{1}{12}​​

D.

512\frac{5}{12}​​

Correct option is C

Given:

Fractions: 23,34,56 \frac{2}{3}, \frac{3}{4}, \frac{5}{6}​​

Formula Used:

HCF of fractions=HCF of numeratorsLCM of denominators\text{HCF of fractions} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}}​​

Solution:
Numerators: 2, 3, 5
HCF(2, 3, 5) = 1

Denominators: 3, 4, 6
Prime factors:

3 = 3

4 = 22 2^2​​

6 = 2×3 \times 3​​
LCM(3, 4, 6) =22×3=12= 2^2 \times 3 = 12​​

HCF=112\text{HCF} = \frac{1}{12}

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