Question

PLEASE HELP!! Somebody please explain to me how LCM(Lowest Common Multiple) works~~
Thanks!! :)

Answer 1

sure. lets pick easy numbers and see how it is done. first of all math does not waste words so your least common multiple must be
a) a multiple of both numbers
b) the smallest one

Answer 2

so if i take some nice small numbers like 6 and 8 i can just guess it is 24 because both 6 and 8 go in to 24 evenly, and 24 is the least number. multiples of 6 are
6, 12, 18, 24, 30, 36, ..
multiples of 8 are
8, 16, 24, 32, 40
and you can see that 24 is in both lists so it is "common" and it is the smallest one

Answer 3

What about 32 & 45?
I know there are stupid ways of figuring this out, but it's not very efficient and I have a Math quiz tomorrow.

Answer 4

ok now it gets a little more complicated. but not in this cases because
\[32=2^5\] and
\[45=3^2\times 5\] and you see they have no factors in common. in math we say they are "relatively prime"

Answer 5

so your LCM is the product of the two numbers, namely
\[32\times 45=1440\]

Answer 6

12&14?

Answer 7

all the work is in factoring the numbers to see which if any factors they have in common. lets try 12 and 14

Answer 8

ok we factor 12 as
\[12=2^2\times 3\]
\[14=2\times 7\] so we are going to need
\[2^2\] and
\[3\] and
\[7\] for our least common multiple
we do not need
\[2^3\] because if we have
\[2^2\] we are good for both 17 and 14

Answer 9

sorry for 12 and 14

Answer 10

would help if i could multiply
our least common multiple is
\[2^2\times 3\times 7=4\times 3\times 7=12\times 7=84\]

Answer 11

it is a multiple of 12 because
\[12\times 7=84\] and it is a multiple of 14 because
\[6\times 14=84\]

Answer 12

Okay, yes, I understand that part. What confuses me is what numbers you should take out of the prime factors to figure out the LCM.

Answer 13

ok all the work is in factoring the numbers. then you take each prime you see to the highest power you see it in any ONE number

Answer 14

for example if i have
\[2^2\times 3^4\times 7\] and
\[2^3\times 3\times 7^2\] my LCM is
\[2^3\times 3^4\times 7^2\]

Answer 15

some times it is obvious. like if i had 30 and 50 i would say 150 right away

Answer 16

OH! Yeah, now I get what prime factors you use to determine the LCM.
OK. Thanks!

Answer 17

good. each prime you see to the highest power you see it in any ONE factor. don't go adding up the exponents!

Answer 18

yw

Answer 19

What if you have one with powers and another one without any powers? Just integers?

Answer 20

if you have
\[3\times 5^2\] and
\[3\times 5\times 7\] you need
\[3\times 5^2\times 7\]

Answer 21

there isn't really "one without powers" if you just see a number the exponent is 1
\[3=3^1\]