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For this you will need a couple of helper algorithms. The first is the GCD (greatest common divisor) which is expressed as follows:
procedure GCD (a, b) is
input: natural numbers a and b
while a<>b do
if a>b
let a be a-b
else
let b be b-a
end if
end while
return a
The second algorithm is the LCM (least common multiple) of two numbers:
procedure LCM (a, b) is
input: natural numbers a and b return (a*b) / GCD (a, b)
Now that you can calculate the GCD and LCM of any two natural numbers, you can calculate the LCM of any three natural numbers as follows:
procedure LCM3 (a, b, c) is
input: natural numbers a, b and c return LCM (LCM (a, b), c)
Note that the LCM of three numbers first calculates the LCM of two of those numbers (a and b) and then calculates the LCM of that result along with the third number (c). That is, if the three numbers were 8, 9 and 21, the LCM of 8 and 9 is 72 and the LCM of 72 and 21 is 504. Thus the LCM of 8, 9 and 21 is 504.
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