HCF and LCM

HCF means Highest Common Factor: HCF of two or more numbers is the greatest number that divides each of them exactly.

We are going to practice question like first simple, little bit tuff and more tuff. Tuff means the question takes more time for calculation that’s it ok. I will give some tips for quicker calculation methods also.

Ex. 1 Find the HCF of 42 and 70

           

42 = 2x3x7

            70 = 2x5x7  HCF = 2x7=14

           

            Quicker method

            70-42=28

            42-28=14

            28-14=14

            14-14=0           HCF =14

Ex. 2 Find the HCF of 1365,1560 and 1755

           

1365=3x5x7x13

            1560=2x2x2x3x5x13

            1755=3x3x3x5x13      HCF=3x5x13=195 in this method we have to spend little bit more time 

Quicker method         

1560-1365=195

            1755-1560=195           HCF = 195

HCF of decimals

Rule first make (if necessary) the same number of decimal places in all given numbers; then find their HCF as if they are integers and mark off in the result as many decimal places as there are in each of the numbers.
Ex 1: Find the HCF of 16.5, 0.45 and 15
  Sol: The given numbers are equivalent to
             16.50, 0.45 and 15.00
          Find HCF 1650,45 and 1500 (remove the dot)
  1650-1500=150
   150-45
     

  LCM means Least common multiple:  The LCM of two or more given numbers is the least number which is exactly divisible by each of them.

Ex. 1 Find the LCM of 8,12,15 and 21

            8=2 x 2 x 2=2³

            12=2 x 2 x 3=2² x3

            15=3 x 5

            21=3 x 7          LCM=2³ x 3 x 5 x 7=840

DIVISION METHOD

3	8	12	15	21
4	8	4	5	7
	2	1	5	7

                       LCM   = 3 x 4 x 2 x 5 x 7=840