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HCF and LCM

HCF and LCM

FACTORS / DIVISORS = Numbers that divide any number completely, without

leaving any Remainder are its factors.

Example : Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

                  Factors of 90 are 1, ,2, 3, 5 , 6, 9, 10, 15, 18, 30, 45, 90

MULTIPLES =  Numbers that fall in tables of any given number are

its Multiples.

Examples  : Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96……

                     Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 …..

HIGHEST COMMON FACTOR (H.C.F.) /  GREATEST COMMON DIVISOR (G.C.D.) = 

Largest number that divides two or more than two given numbers.

Examples : Calculate the  H.C.F. of 45 and 27 

Sol : Factors of 45 = 1, 3, 5, 9, 15, 45

        Factors of 27 = 1, 3, 9, 27

        Hence H.C.F. of 45 and 27 are 9.

Examples : Calculate the H.C.F. of 20 and 88.

Sol : Factors of 20 = 1, 2, 4, 5, 10, 20

        Factors of 88 = 1, 2, 4, 8, 11, 22, 44, 88

        Hence H.C.F. of 20 and 88 are 4.

LEAST COMMON MULTIPLE (L.C.M.) = Least number which is exactly divisible by each of

the given numbers.

Example : Calculate the L.C.M. of 12 and 18.

Sol : Multiples of 12 = 12, 24, 36

        Multiples of 18 = 18 , 36

        Hence L.C.M. of 12 and 18 are 36

Alternate Method : PRIME FACTORIZATION APPROACH

Prime Factorization of 12 = 2² x 3¹

Prime Factorization of 18 = 2¹ x 3²

Hence the  L.C.M. of 12 and 18 are 2² x 3² = 36


Example : Calculate the L.C.M. of 25 and 45

Sol : Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225

         Multiples of 45 = 45, 90, 135, 180, 225

        Hence L.C.M. of 25 and 45 are 225

Alternate Method : PRIME FACTORIZATION APPROACH

Prime Factorization of 25 = 5² 

Prime Factorization of 45 = 3² x 5¹ 

Hence the  L.C.M. of 12 and 18 are 3² x 5² = 225


  • The product of two numbers is always equal to the product of their H.C.F.and L.C.M. 

                                H.C.F. x L.C.M. = A x B

  • H.C.F. of co-prime = 1.

  • To calculate the H.C.F. and L.C.M. of fractions :

                                                H.C.F. of Numerators

  • H.C.F. of Fractions = ━━━━━━━━━━━

                                   L.C.M. of Denominators

                                                L.C.M. of Numerators

  • L.C.M. of Fractions = ━━━━━━━━━━━

                                    H.C.F. of Denominators

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