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 a^{b}_{c}^{
} of a calculator to help
find the HCF and LCM.
·
Input the fraction 36/100 with the key a^{b}_{c}:
36 a^{b}_{c} 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 è
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 can’t simplify any more (be sure!) 

96 
48 
16 
Therefore HCF =
42¸7 = 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 §