
Shortcut Trick
Convert all fractions to their simplest irreducible form: 3/4, 6/8 → 3/4, and 9/10.
Shortcut formula: LCM of Fractions = LCM of Numerators ÷ HCF of Denominators.
Numerators are 3 and 9 ⇒ LCM(3, 9) = 9.
Denominators are 4 and 10 ⇒ HCF(4, 10) = 2.
Required LCM = 9/2.
∴ The correct answer is 9/2.

Alternate Method
Given: The fractions are 3/4, 6/8, and 9/10.
Formula Used: LCM of fractions = [LCM of Numerators] ÷ [HCF of Denominators]

⇒ First, simplify the given fractions to their lowest terms: 3/4 remains 3/4, 6/8 becomes 3/4, and 9/10 remains 9/10.
⇒ Identification of terms: Numerators = 3, 3, 9; Denominators = 4, 4, 10.
⇒ Calculate the Least Common Multiple (LCM) of the Numerators: LCM(3, 3, 9) = 9.
⇒ Calculate the Highest Common Factor (HCF) of the Denominators: HCF(4, 4, 10) = 2.
⇒ Applying the formula: LCM = 9/2.
∴ The correct answer is 9/2.

Additional Information
HCF of Fractions
The Highest Common Factor of fractions is calculated as: HCF of Fractions = (HCF of Numerators) ÷ (LCM of Denominators).
Simplification Rule
Before calculating the LCM or HCF of any group of fractions, it is mandatory to reduce every fraction to its lowest terms (simplest form) to avoid incorrect results.
Fundamental Definitions
LCM is the simplest positive integer divisible by all numbers in a set, while HCF is the largest positive integer that divides all numbers in the set without leaving a remainder.