Master HCF & LCM with Vedic difference tricks, fraction rules, bell tolling interval formulas, and 2-number product identities.
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Learn Prime Factorisation, Long Division, and Vedic Difference Methods.
⚡ Vedic Difference Method for HCF
Rule: The HCF of any set of numbers must divide their difference.
Step 1: Take the minimum difference between any two numbers.
Step 2: HCF is either that difference or a factor of that difference!
Example: HCF(414, 483) → Difference = 483 − 414 = 69. 69 divides both, so HCF = 69.
📚 Fraction HCF & LCM Formulas
HCF of Fractions
(HCF of Numerators) / (LCM of Denominators)
HCF(2/3, 8/9, 16/27) = 2 / 27
LCM of Fractions
(LCM of Numerators) / (HCF of Denominators)
LCM(2/5, 4/15, 6/25) = 12 / 5
Solve traffic signal, bell tolling, and remainder word problems.
Bells Coinciding Rule: Bells with intervals t₁, t₂, t₃ toll together every LCM(t₁, t₂, t₃) seconds. In time T, total tolls = ⌊T / LCM⌋ + 1 (including start).
📊 Remainder Problem Models
| Problem Type | Formula Solution |
|---|---|
| Smallest number leaving remainder r | Answer = LCM(A, B, C) + r |
| Smallest number with constant diff k = (A - r₁) | Answer = LCM(A, B, C) - k |
| Largest number leaving remainder r | Answer = HCF(A - r, B - r, C - r) |
Master HCF-LCM product properties and co-prime ratio relationships.
🏆 Two-Number Product Identity
Product Identity: HCF(a, b) × LCM(a, b) = a × b.
Ratio Form: If numbers are in ratio x : y with HCF = h, then numbers are h·x and h·y, and LCM = h·x·y.
12 competitive questions testing HCF, LCM, fractions, and interval coincidence.
