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

Question 824407: Is the LCm of a pair of numbers ever less than both numbers? Explain with an example.
Answer by KMST(5328) (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,
for some positive integer ,
so ,
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 ,
and if both numbers were the same,
it would be equal to both,
as in .

RELATED QUESTIONS
Is the LCM of a pair of numbers ever equal to one of the numbers? Explain with an... (answered by stanbon)

Is the GCF of a pair of numbers ever greater than both numbers? Explain with an... (answered by stanbon)

Is the GCF of a pair of numbers even equal to one of the numbers? Explain with an... (answered by Edwin McCravy)

explain how to identify the gcf and lcm of a pair of number if one number is a factor of... (answered by richard1234)

Is the LCM of two numbers always divisible by the GCF of the two numbers? If so why. If... (answered by RAY100)

1. the product of an integer and 5 is greater than -32. find the least integer that makes (answered by Edwin McCravy,ikleyn)

The LCM of 2 consecutive numbers is greater than 200 and is a multiple of seven. Name the (answered by stanbon)

Is this an example of a function ? If no explain If yes explain? The assignment of... (answered by Fombitz)

please help me answer Explain what domain and range are, Under what circumstances... (answered by solver91311)