LCM & HCF

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                                                                        LCM and HCF

 

Highest Common Factors (HCF)

Suppose there are three numbers 6, 12 and 30, can you tell highest common factor of these three numbers?  Remember the following steps to find HCF:

  • Determine the factors of given numbers
  • Then, find the common factors among the numbers
  • Among the factors, Highest factor is the required number which is HCF of the given numbers
  • If there is no common factor then 1 is HCF of the given numbers

 So, the factors of 6 are 1, 2, 3 and 6

The factors of 12 are 1, 2, 3, 4, 6 and 12.

The factors of 30 are 1, 2, 3, 4, 5, 6, 10, 15 and 30.

The common prime factors of 6, 12 and 30 are 1, 2, 3 and 6.

However, the highest common factor among these is 6. So 6 is the HCF of 6, 12 and 30.

 

The highest common factor (HCF) of two whole numbers
is the largest whole number which is a factor of both.
 

Another method to determine HCF is division method. The steps to find HCF are:

  • Divide the Highest number by lowest number
  • The last divisor is the HCF of the given numbers

Example: Determine of HCF of 24 and 36 by division method.

Solution: 24)36(1
                       24
                 12)24(2
                      24       
                       0

Hence, last divisor is 12. Thus 12 is the HCF of 24 and 36.    

 

 

Lowest Common Multiple (LCM)

We know,
        Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65…
        Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78….
        Multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130…

 

As we can see the common multiples of 5, 6 and 10 are 30 and 60. The lowest among them is 30. So, 30 is the LCM of 5, 6 and 10.

So, the steps to determine LCM are:

  • Determine the multiples of the given numbers
  • Find the common multiples of the given numbers
  • The lowest of the common multiples is the required LCM of given numbers.

 

The lowest common multiple (LCM) of two whole numbers
is the smallest whole number which is a multiple of both.
 

Another method to find LCM is Euclid’s Method.

Example: Find the LCM of 14, 34, and 21 by Euclid’s method.

 2 |14, 34, 21

    7 |7, 17, 21

           1, 17, 3

The required LCM of 14, 34 and 21 is 2x7x17x3 = 714.

 

The Steps to determine LCM by Euclid’s method:

  • Divide the given numbers by lowest number
  • This division process will continue up to which it can be divided
  • At last, multiply the divisor numbers and the result found will be the required LCM

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