LCM Kya Hai?
Masalan 4 aur 6 ka LCM 12 hai — kyun ke 12 wo choti se choti taadad hai jo 4 se bhi poori taqseem hoti hai (12 ÷ 4 = 3) aur 6 se bhi (12 ÷ 6 = 2).
Tareeqa 1: Listing Method (Chotay Numbers Ke Liye)
Dono numbers ke multiples likhein, pehla mushtarik multiple hi LCM hai:
4 ke multiples: 4, 8, 12, 16, 20...
6 ke multiples: 6, 12, 18, 24...
Pehla mushtarik = 12 → LCM(4, 6) = 12
6 ke multiples: 6, 12, 18, 24...
Pehla mushtarik = 12 → LCM(4, 6) = 12
Tareeqa 2: Prime Factorization (Baray Numbers Ke Liye)
Step 1: Prime Factors Nikalein
12 = 2 × 2 × 3
18 = 2 × 3 × 3
18 = 2 × 3 × 3
Step 2: Har Prime Ki Zyada Se Zyada Power Lein
2² (12 se) × 3² (18 se) = 4 × 9 = 36
LCM(12, 18) = 36
LCM(12, 18) = 36
LCM Aur GCF Mein Farq
- LCM = choti se choti mushtarik multiple (12 aur 18 ka LCM = 36)
- GCF = bara se bara mushtarik divisor (12 aur 18 ka GCF = 6)
Dono ka rishta: LCM × GCF = dono numbers ki zarb
36 × 6 = 216 = 12 × 18 ✓
LCM Kahan Kaam Aata Hai?
- Fractions jorna: Mukhtalif denominator wali kasron ko jorne ke liye LCM chahiye
- Time problems: "Do ghariyan kab ikathi bajengi?" — LCM ka sawal hai
- Tests/Exams: NTS, CSS, entry tests mein laazmi topic
Common Sawalat
Teen numbers ka LCM kaise nikalein?
Wohi tareeqa — teenon ke prime factors nikalein, har prime ki max power lein, zarb kar dein. Masalan LCM(4, 6, 8) = 24.
Kya LCM hamesha numbers se bara hota hai?
Aksar haan, lekin jab aik number doosre ka multiple ho to bara number hi LCM hota hai — masalan LCM(4, 8) = 8.
GCF kaise nikalein?
Prime factors mein jo mushtarik hon, un ki kam se kam power lein. Hamara LCM & GCF calculator dono aik saath nikalta hai.
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Numbers daalein — LCM aur GCF foran, steps ke saath.
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