Question

What's the difference between least common multiples and least common denominators?

Answer 1

the least common denominator of two fractions is the least common multiple of the denominators

Answer 2

So they're the same?

Answer 3

for example, the least common multiple of 8 and 12 is 24, so the least common denominator of
\[\frac{7}{8}\text { and }\frac{5}{12}\] is 24

Answer 4

How do you find lcm?

Answer 5

depends on how annoyingly large the numbers are

Answer 6

I doubt they will be annoyingly large. This is just review, which I am failing at.

Answer 7

if they are small you can usually guess and check. if they are large, like say 84 and 98 you have to factor each one into products of primes, and then take each prime you see to the highest power you see in any one number

Answer 8

So I'm subtracting two fractions. I do prime factorization? Then what do I use GCF for?

Answer 9

so for 8 and 12 i could say
\[8=2^3,12=2^2\times 3\implies \text{lcm} =2^3\times 3=24\]

Answer 10

if you want, and the numbers are not too large, you can always use
\[\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}\] and cancel at the end

Answer 11

for example
\[\frac{3}{4}-\frac{1}{3}=\frac{3\times 3-4\times 1}{4\times 3}=\frac{9-4}{12}=\frac{5}{12}\]

Answer 12

7/12 -3/8. So I would prime factorize? And then that would find me the LCM... ?

Answer 13

we already found the lcm of 8 and 12 is 24

Answer 14

.... WAT. I know.

Answer 15

Just confused.

Answer 16

so you would write
\[\frac{7}{12}=\frac{2\times 7}{24}=\frac{14}{24}\] and
\[\frac{3}{8}=\frac{3\times 3}{24}=\frac{9}{24}\] and so
\[\frac{7}{12}-\frac{3}{8}=\frac{14}{24}-\frac{9}{24}=\frac{5}{24}\]

Answer 17

OH

Answer 18

right, i did it the lcm way, not the other way

Answer 19

Okay, I'm an idiot. Sorry.

Answer 20

no i am sure you are not an idiot
fractions are annoying

Answer 21

the other way is lcd... I think?

Answer 22

lcd is the same as lcm, that is you find the lcm of the two denominators and that is your lcd

Answer 23

Okay, so... I find the lcm of the two denominators by using prime factorization, and once I find that number I kjdfasoudfasuasajsa. Right?

Answer 24

i guess...