Compute the LCM of three fractions step by step Find the least common multiple (LCM) of the fractions 3/4, 6/7, and 9/8 using LCM(numerators) / HCF(denominators).

Introduction / Context:
LCM for fractions reduces to one LCM on integers and one HCF on integers. This avoids unwieldy conversions to common denominators for each fraction.

Given Data / Assumptions:

• Fractions: 3/4, 6/7, 9/8.
• Rule: LCM(fractions) = LCM of numerators / HCF of denominators.

Concept / Approach:
Find LCM(3, 6, 9) and HCF(4, 7, 8) separately, then divide the former by the latter.

Step-by-Step Solution:
LCM of numerators: LCM(3, 6, 9) = 18.HCF of denominators: gcd(4, 7, 8) = 1 (since 7 is coprime to both 4 and 8).Therefore LCM of fractions = 18 / 1 = 18.

Verification / Alternative check:
(18) ÷ (3/4) = 24; (18) ÷ (6/7) = 21; (18) ÷ (9/8) = 16. All quotients are integers, confirming 18 works for all three.

Why Other Options Are Wrong:
3, 6 are too small to be common multiples for all three. 3/56 and 9/28 misapply the fraction-HCF rule or invert the intended formula.

Common Pitfalls:
Interchanging the two rules (HCF vs LCM), or assuming you must first find a common denominator across all fractions.

Final Answer:
18