NUMBERS AND MEASURES

HCF (Highest Common Factor) and LCM (Lowest Common Multiple):

 

SHORTCUT METHOD: Using quotient (fraction) and calculator (if we can)

 

Example 1: Find the HCF and LCM of 120 and 36

 

Answer: To find the HCF and LCM we make a fraction - smaller number is the top,

bigger number is the bottom - and simplify as much as we can:

 

 

Then

      HCF = 36 3 or 120 10. Both calculations produce HCF = 12.

      LCM = 36 10 or 120 3. Both calculations produce LCM = 360

 

Using calculator

 

We can use the key abc of a calculator to help find the HCF and LCM.

        Input the fraction 36/100 with the key abc: 36 abc 120 and press =.

The calculator produces the irreducible equivalent fraction 3/10

        Divide big top by small top and you have got the HCF. (You can also divide the big bottom by small bottom.)

        Multiply big top by small bottom or big bottom by small top and you have got the LCM.

 

Relationship between the LCM and the HCF

 

To find the LCM or HCF we can use the fact that for any two numbers a and b their product is the same as the product of their HCF and LCM.

a b = HCF LCM

 

                  LCM = ab/HCF and HCF = ab/LCM

 

 

Example 2. Find the HCF and LCM of 42 and 96.

Answer: We make a fraction and simplify it as much as we can:

 

 

42

=

21

=

7

 

We cant simplify any more (be sure!)

 

96

48

16

 

Therefore HCF = 427 = 6

LCM = 42 16 = 672.

It is advisable to double check HCF = 6 = 96 16. YES. LCM = 672 = 96 7 YES.

Or triple check; 42 96 = 6 672? YES. Both produce 4032