What is the LCD ?

45 = 3 x 3 x 5
105 = 3 x 5 x 7
--------------------
The LCD of 45,105 is:
3 x 3 x 5 x 7
= 315

Prime factors:

45= 3² * 5
105 = 3 * 7 * 5

LCD is every factor that exists between the two. If any are shared (in this case, the 3 and 5), only count it once:

LCD = 3² * 7 * 5 = 315

At least three things that I know about are abbreviated LCD. Liquid Crystal Diode is one, which is an electronic technology used in the production of high definition video displays. That is what I thought you were talking about until I clicked on the question and discovered the other half of it. You were talking about a different LCD, either Lowest Common Denominator or Lowest Common Divisor. I will attempt to answer Lowest Common Divisor. So what is the Lowest Common Divisor of 45 and 105?
The simple answer is that the LCD is the lowest number that will divide evenly into both of them, which is not a 1. You don't count 1, because it goes into every number evenly. So how do you find it? Well, you can't divide 45 or 105 by 2, can you? How do I know that? It is because 45 and 105 both end in a 5, which makes them odd numbers, not even numbers like 4, 16, 32, 98, etc. So a 2 will not go into 45 or 105 without a fraction left over. So, what about a 3? Will a 3 go into both 45 and 105? Yes! It will go into the first number 15 times... and it will go into the second number 35 times. Ah-ha! Then the LCD Lowest Common Divisor of 45 and 105 is 3.

There is another LCD called Lowest Common Denominator, but I will not try to answer that one this time.

lcm(45, 105)=315

3 45 , 105
5 15 , 35
3 3 , 7
7 1 , 7
1 , 1

LCD of 45 and 105 is 3x3x5x7

LCD is the same as LCM, so

5 | 45 105
-----------
----9 21
-----------
3 | 3 7
-----------

Therefore, LCD(45,105) = 5*3*3*7 = 315

I have some notes that I made for my students:

http://www.scs.gmu.edu/~mwester1/lcm.pdf

_________________
5/ 45 , 105

Just divide. I chose 5 because it is obvious that 45 and 105 is divisible by 5.

You get 5 and 13. There is nothing common between these number.

Now just multiply them all (5 x 5 x 13)
You get 325 as the LCD.

105 * 3 = 315
45 * 7 = 315

LCD = 315

LCD of 45 and 105

Factor 45: 3x3x5
Factor 105: 3x5x7

LCD = 3x3x5x7 = 315

315