H.C.F. & L.C.M.
View Questions of H.C.F. & L.C.M.
Quantitative Aptitude - H.C.F. & L.C.M.
Understand, apply, and solve quickly to score easy marks.
1. What are H.C.F. and L.C.M.?
- H.C.F. (Highest Common Factor): Greatest number that divides all given numbers exactly.
- L.C.M. (Least Common Multiple): Smallest number that is divisible by all given numbers.
2. Relationship Between H.C.F. and L.C.M.:
\[ \text{H.C.F.}(a,b) \times \text{L.C.M.}(a,b) = a \times b \]
3. Methods to Calculate:
- Prime Factorization: Express numbers as products of primes; take minimum powers for H.C.F., maximum for L.C.M.
- Division/Ladder Method: Divide both numbers by common primes step by step until no common divisors left.
4. How to Solve Word Problems:
- If objects/events repeat after certain cycles, use L.C.M. to find the repetition interval.
- If multiple groups divide things equally, use H.C.F. to determine maximum equal group size.
5. Tips to Answer Quickly:
- Start with H.C.F.; then use the formula to find L.C.M. to save time.
- For more than two numbers, combine stepwise: H.C.F.(a,b,c) = H.C.F.(H.C.F.(a,b), c).
- Use divisibility shortcuts (for 2,3,5,7) to speed up prime factorization.
- Keep factor tables ready for small primes (2,3,5,7,11).
6. Typical Exam Questions:
- Find H.C.F. and L.C.M. of multiple numbers.
- Find least value divisible by given numbers.
- Find maximum size or count in division problems.
7. Revision Checklist:
- Know the identity: H.C.F. × L.C.M. = product of numbers.
- Be fluent in prime factorization up to at least 100.
- Practice at least 15 H.C.F./L.C.M. problems every week.
Summary: Break numbers into primes, identify common and uncommon powers, apply the identity, and use H.C.F./L.C.M. logic in word problems for fast and accurate solutions.
Topics
- Number System
- H.C.F. & L.C.M.
- Decimal Fractions
- Simplification
- Square Roots & Cube Roots
- Average
- Problems on Numbers
- Problems on Ages
- Surds & Indices
- Percentage
- Operations on Numbers
- Profit & Loss
- Ratio & Proportion
- Partnership
- Chain Rule
- Time & Work
- Pipes & Cistern
- Time & Distance
- Problems on Trains
- Boats & Streams
- Alligation or Mixture
- Simple Interest
- Compound Interest
- Logarithms
- Area
- Volume & Surface Areas
- Mensuration
- Races & Games of Skill
- Calendar
- Clocks
- Stocks & Shares
- Permutations & Combinations
- Probability
- True Discount
- Banker’s Discount
- Heights & Distances
- Odd Man Out & Series
- Algebra
- Divisibility Rules & Remainder Theorem
- Factorials & Power Cycles
- Progressions (A.P., G.P., H.P.)
- Work & Wages
- Set Theory / Venn Diagrams
- Geometry (Lines, Angles, Triangles, Polygons)
- Coordinate Geometry
- Data Interpretation
- Trigonometry
- Statistics (Mean, Median, Mode)
- Arithmetic Operations
- Quadratic Equations