Question

What is the greatest number which can divide $\frac{4}{5},\frac{5}{6}\&\frac{6}{7}$ leaving a remainder zero with integer quotients?

• A. $\frac{1}{210}$
• B. 210
• C. $\frac{1}{7}$
• D. $\frac{6}{7}$

Answer 1

The correct option is A

$\frac{1}{210}$

Highest common factor (HCF) of two or more numbers is the greatest number which divides each of them exactly.
To get the greatest number which can divide $\frac{4}{5},\frac{5}{6}\&\frac{6}{7}$ leaving a remainder zero with integer quotients, the HCF of the given numbers is to be found.
HCF of fractions $=\frac{\text{HCF of numerators}}{\text{LCM of denominators}}$
HCF of numerators 4, 5 and 6 = 1
LCM of denominators 5, 6 and 7 = 210
HCF of the given numbers $=\frac{1}{210}$