SOLUTION: Is the LCm of a pair of numbers ever less than both numbers? Explain with an example.

Algebra ->  Finance -> SOLUTION: Is the LCm of a pair of numbers ever less than both numbers? Explain with an example.      Log On


   

Question 824407: Is the LCm of a pair of numbers ever less than both numbers? Explain with an example.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The usual definition of least common multiple of two numbers states that it is the least positive integer that can be evenly divided by both numbers. The way it is usually defined the two numbers must be positive integers.
LCM(3,5) must be a number divisible by 2 and by 5.
As it must be divisible by 5,
LCM%282%2C5%29=5%2An for some positive integer n%3E=1 ,
so LCM%282%2C5%29=5%2An%3E=5%3E2 ,
As in the example above, the LCM has to be equal to or greater than the greater of the two numbers.
It never could be less than both numbers.

The LCM could be equal to one of the numbers,
as in LCM%282%2C6%29=6 ,
and if both numbers were the same,
it would be equal to both,
as in LCM%287%2C7%29=7 .