LCM and HCF short tricks ki jankari hindi me

Hello friends, Mathsmell me aapka swaghat hai. Previous post me humne jana ki lcm and hcf prime factorization and division method me kaise karte hai.Inn dono methods help se kisi bhi numbers ki lcm and hcf nikal sakte hai. Lekin competitive exams me kam samai me questions solve karna hai. isliye aaj iss post hum janenge lcm and hcf ki some important shortcut tricks in hindi aur iss sabhi short tricks ki madad se aap  lcm and hcf se related koi bhi questions ki solution sirf 5 seconds me karpayenge.

Short tricks of LCM and HCF with example hindi me:
Dosto hum sab jante hai lcm ki full form least common multiple and hcf ki full form hai highest common factor.dosto ek baat aur ki all competitive exams me lcm and hcf se questions puche jate hai.To chaliye dekhlete hai lcm and hcf ki short tricks in hindi.

TRICKS-1.
Product of two number = LCM * HCF

Ex.1: The LCM of two numbers is 63 and their HCF  is 9 ,if the first number is 27, then find the second number.
Soln. Here LCM = 63, HCF = 9, 1st number = 27.
According to the tricks,
Product of two number = LCM * HCF
27 * 2nd number = 63 * 9
2nd number = (63*9)/27 = 21.
Therefore, second number = 21.

TRICKS - 2.

 LCM of fractions = LCM of numerators / HCF of denominators.

Example: Find the LCM of 36/125 , 42/25, 54/55.
Soln. Sabse pehle numerators ki lcm kare.
Lcm of 36, 42, 54 = 756.
Next, denominators ki HCF kare.
HCF of 125, 25, 55 = 5.
Next, lcm ko hcf se divide kare. 756/5 151.2
Therefore lcm of fractions = 151.2

TRICKS- 3.

HCF of fractions = HCF of numerators / LCM of denominators.

Ex: Find the hcf of 12/17 and 60/17.
Soln. Hcf of 12 and 60 = 12
LCM of 17 and 17 = 17.
According to the tricks,
HCF = 12/17.

TRICKS-4.

Leargest or greatest number which divides the numbers a, b and c, leaves the remainders p, q and r respectively is given by = HCF of (a-p), (b-q), (c-r).

OR Agar kisi greatest number ko a, b and c se divide kare and remainders p, q and r hua to greatest number = HCF of (a-p), (b-q), (c-r).

Ex. Find the largest number that divides 130, 305 and 245 leaving remainders 6, 9 and 17 respectively.
Soln. Here a = 130, b = 305, c = 245 and p= 6, q = 9, r = 17.
So largest number = HCF of (a-p), (b-q), (c-r).
= hcf of (130 - 6), (305 - 9), (245-17).
= hcf of 124, 296, 228.
= 4.

TRICKS- 5.
Largest or greatest number which divides the numbers a, b and c leaves the same remainder is given by HCF of (a - b), (b - c),  (c - a).
OR
Agar kisi largest or greatest number se a, b and c ko divide kare and her bar remainder same hua to,  Number = Hcf of (a - b), (b - c),  (c - a).

Example: What is the greatest number that divides 99, 123 and 183 leaving the same remainder in each case ?
Soln. Here a = 99, b = 123 and c = 183.
Therefore greatest number = Hcf of (a - b), (b - c),  (c - a).
= Hcf of  (99 - 123), (123 - 183), (183-99)
= Hcf of 24, 70, 84.
= 12 ; hamesa +ve value lena hai.

TRICKS - 6.
Smallest or least number which divides the numbers a, b and c, leaves the remainders p, q and r respectively is given by = [LCM of ( a, b, c) - k].

OR

Agar koi least number ko a, b and c se divide kare and remainder p, q and r hua to bho least number = [LCM of ( a, b, c) - k]. Here k = a - p = b - q = c - r.

EX: - Find the least number which when divided by 24, 32 and 36 leaves the remainders 19, 27 and 31 respectively.
Soln. Here a = 24,  b = 32,  c = 36 and p = 19,  q = 27,  r = 31.
Also, K = a - p = b - q = c - r.
= 24 -19 = 32 - 27 = 36 - 31 = 5.
Least number = LCM of ( a, b, c) - k
= Lcm of (24, 32, 36) - 6.
= 288 - 5 = 283.

TRICKS - 7.
Smallest or least number which divides the number a, b and c leaves the same remainder k is given by = LCM of (a, b, c) + k.
OR
Agar kisi number ko a, b and c se divide kare and harber remainder k hua to
Least number = LCM of (a, b, c) + k.

Ex:- The least number which when divided by 12, 16 and 18 leaves 5 as remainder in each case. find the number.
Soln. Here a = 12,  b = 16, c = 18 and k = 5.
Least number = LCM of (a, b, c) + k.
                         =lcm of (12, 16, 18) + 5
                         = 144 + 5
                         = 149.

Dosto upar diye gaye lcm and hcf tricks ki help se aap koi bhi questions ki solution asani se karpayenge.

I hope LCM and hcf shortcut tricks with example in hindi 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 se related questions ki solutions shortcut tricks ki help se kaise karte hai.Thank You...