True or false problem

[karliekay]

Classify each of the follwing as true or false:

I. If a and b are different integers, the least common multiple of a and b is (axb)
II. If a is an even integer and b is an odd integer, the greatest common divisor can not be 6.
III. If a is a divisor of b, then the least common multiple of a and b is b.
IV. If 8 is a divisor of a, then 4 is a divisor of a.

I need help with figuring out the 1st one and seeing if what I got for the rest is right?

I.
II. True
III. True
VI. False

 

[Denis]

I. If a and b are different integers, the least common multiple of a and b is (axb)
I need help with figuring out the 1st one .

Hint: LCM(3,2) = 6 but LCM(6,4) = 12

 

[BigGlenntheHeavy]

\(\displaystyle IV \ is \ true, \ not \ false, \ to \ wit:\)

\(\displaystyle 8|a \ \implies \ a \ = \ 8k, \ k \ an \ integer.\)

\(\displaystyle a \ = \ 8k, \ a \ = \ (4)(2)(k), \ a \ = \ 4(2k), \ let \ 2k \ = \ n, \ n \ an \ integer, \ then \ a \ = \ 4n\)

\(\displaystyle so \ 4|a.\)