# lcm

• Mar 7th 2007, 03:17 PM
diamond1
lcm
whats the LCD of both of these fractions, and what is the equivalent fraction for each fraction? is it <, >, = please help

7/12, 11/18

- 11/20, - 22/40

15/28, 4/7

5/17, 15/51

whats the LCM of the numbers
7, 21

15, 50

28xy^2, 42x^2y

im sorry its so much, if u cant do it all i understand thanx any way, you're a big help!:D
• Mar 7th 2007, 05:33 PM
topsquark
Quote:

Originally Posted by diamond1
whats the LCM of the numbers
7, 21

15, 50

28xy^2, 42x^2y

Let's start here. The LCD of two fractions is just the LCM of the two denominators.

7, 21
Just by inspection you can see that the LCM is 21. Why? Because 21 is a multiple of 7. This one's too easy to demonstrate the method on.

15, 50

Find the prime factorization of both numbers:
15 = 3*5
50 = 2*5^2

Now, the LCM will contain ALL the prime factors of each number, only as many times as it shows up in the prime factorization.

So the LCM contains one factor of 2, one factor of 3, and two factors of 5. Thus:
LCM = 2*3*5^2 = 150.

28xy^2, 42x^2y

We can't find prime factorizations of x and y since we don't know these numbers. So for the purposes of finding an LCM we treat them as if they were prime.

28xy^2 = 2^2*7*x*y^2
42x^2y = 2*3*7*x^2*y

Thus
LCM = 2^2*3*7*x^2*y^2 = 84x^2y^2

-Dan
• Mar 7th 2007, 05:38 PM
topsquark
Quote:

Originally Posted by diamond1
whats the LCD of both of these fractions, and what is the equivalent fraction for each fraction? is it <, >, = please help

7/12, 11/18

- 11/20, - 22/40

15/28, 4/7

5/17, 15/51

If I understand what you want, I will express each fraction with the same denominator, then say which of <, >, or = is true.
7/12, 11/18

LCM of 12 and 18 = 36
7/12 = 21/36
11/18 = 22/36

So
7/12 < 11/18
=================

- 11/20, - 22/40

LCM of 20 and 40 = 40
-11/20 = -22/40
-22/40 = -22/40

Thus -11/20 = -22/40
=================
15/28, 4/7

LCM of 28 and 7 = 28
15/28 = 15/28
4/7 = 16/28

Thus
15/28 < 4/7
=================

5/17, 15/51

The LCM of 17 and 51 = 51
5/17 = 15/51
15/51 = 15/51

Thus
5/17 = 15/51

-Dan
• Mar 7th 2007, 05:44 PM
diamond1
thanx
thank u sooooooooooo much dan