Basic concept of LCM and HCF with examples in hindi

Hello friends, welcome to mathsmell. LCM and HCF mathematics ki bahu he important part hai.LCM ki full form hai Least common multiple and HCF ki fulform hai Highest common factor.Sabhi competitive exams me lcm and hcf se questions puche jate hai aur hum sab lcm and hcf ki shortcut tricks apply karke exams me questions ki solution karte hai lekin basic concept aur lcm and hcf ki sahi meaning pata nahi hone ki karan tricks vul jate hai and questions ke solution nahi kar pate.

Isliye aaj iss poat me hum janenge what is the fullform of lcm and hcf,lcm kya hai,hcf kya hai,hcf meaning in hindi, lcm meaning in hindi.

Isliye dosto iss post ko dhayan se pura read kare taki lcm and hcf se related sari confusion sur hojaye.

Baaic concept of lcm and hcf in hindi:
Lcm ki fullform hai Least common multiple and Hcf ki fullform hai Highest common factor orthat lcm and hcf ki bare me janne se pehle hume janna hoga multiple, common multiples, factors and common factors ki definition ki bare me.

Multiples kya hai:
Set of number which are exactly divisible by given number or jis number ki multiples nikal na hai, uss number ko 1,2, 3,.....  se gunna kare, gunna karne ke baad jho numbers milegi uss sabhu numbers ko given number ki multiples kehte hai.
For examples:
Multiples of 2 = { 2, 4, 6, 8, 10,.......... etc}
Multiplea of 3 = { 3, 6, 9, 12, 15,....... etc.}
Multiples of 4 = { 4, 8, 12, 16, 20,..... etc.}

NOTE: Multiple of a number are always more than or equal to the given number or kisi bhi numbers ki multiples ki sankhaya hamesha uss numbers ki equal ya usse jada hoga.

Common multiples kya hai:
Two ya two se jada numbers ki multiples ki ander jho multiples dono numbers ki hote hai, usse common multiples kehte hai.

Example: Find the common multiples of 2 and 3.
Soln. Sabse pehle 2 and 3 ki multiples nikaliye.
Multiples of 2 = { 2, 4, 6, 8, 10,.......... etc}
Multiplea of 3 = { 3, 6, 9, 12, 15,....... etc.}

Next 2 and 3 ki common multiples nikalne ke liye 2 and 3 ki multiples me jho common numbers hai usse likhiye. Jaise 2 ki multiples hai 6,  12 and 3 ke bhi multiples hai 6, 12.So 6, 12 are common multiples of 2 and 3.
Common multiples of 2 and 3 = { 6, 12, 18,...... etc.}.

LCM- Least common multiple:
Hum jangaye ki multiples and common multiples kya hai.Abb hum janenge what is lcm in hindi and definition of lcm in hindi.
Lcm ki meaning hai least common multiple and least ka matlab hote hai sabse chota orthat lcm ka actual meaning hai sabse chota common multiples.

So two ya two se jada numbers ki lcm find karne ke liye sabse pehle dono numbers ki multiples nikaliye, next common multiples nikalna hai and finally sabse chota common multiple or LCM find karna hai.

Ex:1. Find the LCM of 3, 4, 12.

Soln. 

Multiple of 3  = { 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ............etc}

Multiple of 4  = { 4, 8, 12, 16, 20, 24, 28, 32, 36,...................etc.}
Multiple of 12 = { 12, 24, 36, 48, 60, 72, 84, 96,.....................etc.}

Therefore, common multiples of 3, 4, 12 = { 12, 24, 36, 48,..............etc}

Yaha sbse chota common multiplie = 12

Therefore, LCM = 12.

Ex.2: Find the LCM of 4 and 6.
Soln.: Multiple of 4  = { 4, 8, 12, 16, 20, 24, 28, 32, 36,...................etc.}
          Multiples of 6 = { 6, 12, 18, 24, 30, 36, 42,.................etc.}
          Common multiples = { 12, 24, 36 ,...............etc}
Therefore LCM = 12

Factors kya hai:
Set of numbers which exactly divides the given number or jis numbers ki factors nikal na hai uss number ko 1, 2, 3,......  se divide kare, divide karne ki baad jho numbers milegi usse given number ki factors kehte hai.

For exames: Factors of 9 = {1, 3, 9}
                       Factors of 10 = { 1, 2, 5, 10}

Common Factors kya hai:
Two ya two se jada numbers ki factors ki ander jho factors dono numbers ki hote hai, usse common factors kehte hai.

Example: Find the common factors of 8 and 20.
Soln. Sabse pehle 8 and 20 ki factors nikaliye.
Factors of 8 = { 1, 2, 4, 8}
Factors of 20 = { 1, 2, 4, 5, 10, 20}

Next 8 and 20 ki common factors nikalne ke liye 8 and 20 ki factors me jho common numbers hai usse likhiye.

Common factors of 8 and 20 = { 1, 2, 4}.

HCF - Highest common factor:
HCF ko greatest common mesure or GCM and Highest common divisor or GCD bhi kehte hai.
Hcf ki meaning hai Highest common factor and highest ka meaning hai sabse bara (large) aurthat HCF ki actual meaning hai sabse bara common factor.

Two ya two se jada numbers ki Hcf nikal ne ke liye sabse pehle dono numbers ki factors nikalna hai, next common factors nikalna hai and finally hcf or sabse bara common factor apne aap nikal jayegi.

FOR EXAMPLES:

EX.1 : Find the HCF of 12, 36, 48.
Soln.: 
          Factors of 12 = { 1, 2, 3, 4, 6, 12 }
          Factors of 36 = { 1, 2, 3, 4, 6, 9, 12, 18, 36 }
          Factors of 48 = { 1, 2, 3, 4, 6, 8,12, 16, 24, 48 }
Therefore common factors = { 1, 2, 3, 4, 6, 12 }.

Sabse bara common factor = 12 , Therefore HCF = 12.

Ex.2: Find the HCF of 12, 15, 18.
Soln.: Factors of 12 = { 1, 2, 3, 4, 6, 12 }
           Factors of 15 = { 1, 3, 5, 15 }
           Factors of 18 = { 1, 2, 3, 6, 9, 18 }
Common factors = { 1, 3 }.

Therefore  HCF = 3.

I hope basic concept of lcm and hcf with examples in hindi post apkp acha laga hoga. agar ha to jarur apne dost ki sath iss post ko social media me share kare taki apki dosto ko bhi pata chale lcm and hcf kya hai, fullform of lcm and hcf in maths, lcm and hcf meaning in hindi, lcm and hcf kaise kare. Next post me hum janenge lcm and hcf find karne method ki puri jankari hindi me. Thank you........