LCM and HCF kaise kare puri jankari hindi me

Hello friends, mathsmell me apka swaghat hai. Previous post me humne jana ki LCM ki full form  hai least common multiple and HCF ki full form hai Highest common factor. Aur bhi jana ki lcm and hcf kya hai, hcf meaning in hindi, lcm meaning in hindi and basic concept of lcm and hcf.

Aaj iss post me hum janenge ki lcm and hcf kaise karte hai. aur dekhenge ki kis method me lcm and hcf nikal te hain.Generally, prime factorisation and division method me hum lcm and hcf nikal ta hai.

Method to calculates LCM ( LCM nikal ne ke tarika):
Hum sab jante hai ki lcm ki full form hai least common multiple or smallest common multiple. Lcm find karne ke liye hum prime factorisation and division method apply karte hai.Niche inn dono method se lcm nikal ne puri tarika diye gaye hai.

Prime Factorization method se lcm kaise kare:
Prime factorisation method ki anusar lcm find karne ki process niche diya gaye hai.

1. Sabse pehle jis numbers ki lcm nikal na hai, uss sabhi numbers ko prime factors me likhiye.
2. Next sabhi numbers ki prime factors ke highest power ko ek sath multiply kare. OR first number ki factors ko multiply ki roop me likhiye and baki sabhi number ki jho factos nahi likhe uss factor ko bhi uss factors ki sath gunna kare.
3. Finally, prime factors ki multiplication he hoga LCM.

Ex:- 1. Find the LCM of 8, 12, 15.
Soln. Sabse pehle 8, 12,  15 ko prime factors me likhe.
          8 = 2  * 2 * 2 = 2^3.
        12 = 2 * 2 * 3 = 2^2 * 3.
        15 = 3 * 5.
Here toal three prime factors hai 2, 3 and 5. 2 ki highest power hai 3 and 3 and 5 ki highest powers hai 1.
Therefore, LCM = 2^3 * 3 * 5 = 8 * 3 * 5 = 120.

Ex:- 2. Find the lcm of 12 and 20 by prime factorization method.
Soln. Here  12 = 2 * 2 * 3 = 2^2 * 3.
                     20 = 2 * 2 * 5 = 2^2 * 5.
Here 2, 3 and 5 three prime factors hai.
Highest power of 2 = 2
Highest power of 3 = 1
Highest power of 5 = 1.

So, LCM = 2^2 * 3 * 5 = 4 * 3 * 5 = 60.

Division method me lcm kaise kare:
Ab hum janenge ki division method me lcm kaise karte hai. Division method ki anusar LCM nikal ne ke liye niche diye gaye step ko follow kare.

1. Sabse pehle sabhi numbers ko ek line me lekhe and commas se separate kare.
2. Next, sabhi numbers ko ek aise prime number se divide kare, taki kam se kam two numbers ko divide kiya jaye.
3. Next, sabhi quotient ko niche likhe and jho numbers divide nahi huye usse bhi niche likhe.
4. Iss process ko bar bar repeat kare,  jab tak niche co-prime number  or 1 na mile.
5. Finally, sabhi factors ko ek sath multiply kare aur ye multiplication he hoga lcm.

Ex:-1. Find the LCM of 15 and 24 by division method.
Soln.

Therefore LCM = 2*2*2*3*5 = 120.

1. Sabse pehle 15 and 24 ko commas se separate kare.
2. Next, Least number 2 se 15 and 24 ko divide kare. 24 ko 2 se divide karke 12 mila and 15, 2 se devide nahi hoga.isliye niche 12 and 15 likhe. agar kuch number divide nahi hua to usse numbers ko niche likhe.
3. Next, 2 se 12 and 15 ko divide kare. 2 se 12 ko divide karke 6 mila and 15, 2 se devide nahi hoga.isliye niche 6 and 15 likhe.
4. Fir 2 se 6 and 15 ko  divide karenge to 3 and 15 milege.
5. Next, least number 3 se 3 and 15 ko divide karenge to 1 and 5 milegi.isliye niche 1 and 5 likhe.
6. Next, least number 5 se divide kare, 1 likhhe and 5 ko 5 divide kiye  to 1 he milegi.
7. Finally sabhi divisors  ko multiply kare aur multiplication he hoga LCM.

Therefore LCM = 2*2*2*3*5 = 120

Method to calculate HCF (HCF kaise kare):
HCF ki full form hai highest common factor. Isse greatest common divisor or GCD and greatest common mesure or GCM bhi kehte hai. Generally, hum hcf prime factorisation and division method se nikal te hai. Niche inn dono method ki bare me datails me diye gaye hain.

Prime factorisation method se hcf kaise kare:
Prime factorisation method ki anusar hcf nikal ne ke liye niche diye gaye step follow kare.

1. Sabse pehle sabhi numbers ko prime factors me likhe.
2. Next, sabhi prime factors me se common least power ko lekar multiply kare.
3. Iss common prime factors ki product he hoga HCF.

Ex:- 1. Find the HCF of 12 and 15
Soln. Sabse pehle 12 and 15 ko prime factors me likhe.
12 = 2 * 2 * 3 = 2^2 * 3
15 = 3 * 5

Here common prime factor is 3 aurthat dono numbers ki prime factors me 3 hai.
Therefore HCF = 3.

Ex:-2. Find the HCF of 24, 30 and 42.
Soln. Factors of 24 = 2 * 2 * 2 * 3
          Factors of 30 = 2 * 3 * 5
          Factors of 42 = 2 * 3 * 7

Here common prime factors hai 2 and 3 or three numbers ki prime factors me 2 and 3 hai.
Therefore HCF = 2 * 3 = 6.

Division method me HCF kaise kare:
Humne jana ki factorisation method se hcf kaise karte hai. Ab hum janenge division method me hcf kaise nikalte hai. Division method ki anusar hcf nikal ne ke liye niche diye gaye step ko follow kare.

1. Sabse pehle large number ko small number se divide kare.
2. Next, Divisor (small number)  ko remainder se divide kare.
3. Iss process ko bar bar repeat kare jab tak remainder me '0' nahi hote.
4. Finally last me jho divisor milegi bho he hoga HCF.

Ex:-1. Find the HCF of 15 and 24.
Soln. Sabse pehle large number ko small number se divide kare.

Therefore HCF = 3.

1. First 24 ko 15 se divide karke remainder 9 mila.
2. Next, 15 ko 9 se divide kare remainder 6 mileia.
3. Next, 9 ko 6 se divide kare remainder 3 milegi.
4. Next, 6 ko 3 se divide kare remainder ' 0 ' milegi.

Here, last divisor is 3, therefore HCF = 3.

I hope method to find lcm and hcf with examples or lcm and hcf kaise nikale puri jankari hindi me post apko acha laga hoga.agar ha to iss post ko apne dosto ki sath share kare taki unhe bhi pata chale lcm and hcf kya hote hai and lcm and hcf kaise nikal te hai.Thank you...