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LCM aur HCF kya hai puri jankari hindi me

LCM and HCF babut hi important topics hai,bahut sare competitive exam me 2 ya 3 question ate hai.aaj hum isse ki bare me jankari hasil karenge.
LCM and HCF ki meaning kya hai?
 L.C.M  ki meaning hai least common multiple aur  H.C.F ki meaning hai highest common factor or Greatest common measure (G.C.M )

LCM aur HCF kya hai puri jankari hindi me
Two ya isse jada numbers ki multiplication ko multiple kehte hai and usse number ko kehte hai factor.
Example: Factor of 20 are 1, 2, 4, 5, 10, 20 . and multiple of 20 are 20, 40, 60, 80, 100 etc.

Least Common Multiple (LCM):
The LCM of two or more given number is the least number which is exactly divisible by each of them.
Example: Find the LCM of 3, 4 and 6.
Soln: Multiple of 3 = 3, 6,9,12,15,18,21,24,27,30.......
         Multiple of 4 = 4,8,12,16,20,24,28........
         Multiple of 6 = 6,12,18,24,30.......
Since Common multiple of 3,4,6 are 12,24........
Therefore, least common multiple 12  i.e. LCM = 12

Highest common Factor (HCF):
The HCF of two or more numbers is the greatest number that divides each of them exactly.
Example: Find the HCF of 12 and 16
Soln: 12 = 2 x 2 x 3
         16 = 2 x 2 x 2 x 2
therefore HCF = 2 X 2 = 4.

Important Formulae: 

  • LCM of a fraction = LCM of Numerators/ HCF of Denominators.
  • HCF of a fraction = HCF of Numerators/ LCM of Denominators.
  • HCF X LCM = Product of the two numbers.
  • LCM = Product of the two number / HCF.
  • HCF = Product of the two number / LCM. 
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