Wo sabse chhota positive integer jo dono ka multiple ho.
Prime factorization se LCM: har prime ki kaun si power leni chahiye?
Highest (max) power jo kisi bhi number mein dikhe.
Prime factorization se HCF: har prime ki kaun si power leni chahiye?
Lowest (min) power (0 agar ek number mein prime absent ho).
Do numbers ke liye HCF × LCM relationship batao.
HCF(a,b) × LCM(a,b) = a × b.
HCF × LCM = a·b kyun hota hai?
Kyunki har prime ke exponent ke liye min(α,β)+max(α,β)=α+β.
12 aur 18 ka LCM nikalo.
22⋅32=36.
Agar HCF(a,b)=6 aur LCM=72, aur a=24, toh b kya hai?
b = (HCF·LCM)/a = (6·72)/24 = 18.
Kya HCF×LCM=product 3 numbers ke liye bhi kaam karta hai?
Nahi — sirf exactly do numbers ke liye.
LCM ke liye max power (min nahi) kyun lete hain?
Taaki result dono se divisible ho, hume har prime ki badi requirement chahiye.
60 aur 72 ka LCM?
360.
Recall Feynman: ek 12-saal ke bacche ko explain karo
Socho do ghariyan hain. Ek har 4 second mein beep karti hai, doosri har 6 second mein. Wo saath mein kab beep karengi? Count karo: 12 seconds — wahi LCM hai. Ise fast nikalne ke liye, har number ko uske prime "building blocks" mein todo (sirf primes jaise 2, 3, 5...). LCM ke liye, kisi bhi number mein jo bhi block ka sabse bada dher dikhe, use lo, taaki dono numbers tumhare dher se ban sakein. HCFshared blocks hain (har ek ka sabse chhota dher). Cool trick: agar tum apne do numbers multiply karo, wahi hoga jab HCF aur LCM ko saath multiply karo — kyunki shared part plus baaki part milke sab kuch exactly ek baar cover karta hai!
