Example: Consider the numbers 8 and 12.
Let us find the L.C.M. of 8 and 12.
8 = 2 x 2 x 2
12 = 2 x 2 x 3
Collect the largest number of occurrence of each prime number.
The largest number of times the factor 2 occurs is three.
The largest number of times the factor 3 occurs is one.
Therefore the L.C.M. is = 2 x 2 x 2 x 3 = 24.
Now let us find the G.C.D. of 8 and 12.
Now, we find the product of G.C.D. and L.C.M.,
that is LCM x GCD = 24 x 4 = 96.
Now we shall find the product of two given numbers.
From the above example, we find that 1st number x 2nd number = LCM x GCD.
Hence, the product of two numbers is equal to the product of LCM and GCD of the two numbers.
On the basis of this relation, we find that:
Directions:Answer the following questions. Also write at least 10 examples of your own.