Question

find the smallest possible integer value of n for which 99n is a multiple of 24.

Answer 1

you want to find the least common multiple of 99 and 24 then

Answer 2

do you know how to factor the numbers into smaller amounts?

Answer 3

LCM

Answer 4

a property you can use is also
\[\frac{ab}{gcd(a,b)} = lcm(a,b)\]
but that tends to be more advanced

Answer 5

yeah, I know.

Answer 6

I know the answer, but I don't the working.

Answer 7

I dont know the working.

Answer 8

hmm, it works upon the factorizations of 99 and 24

Answer 9

do you know about prime numbers?

Answer 10

yeah, I do.

Answer 11

all integers have a unique prime factorization of integers. This helps us to know what they have in common, and what they would need as well

Answer 12

what is the prime factorization of primes for 99?

Answer 13

wait.

Answer 14

3x3x11

Answer 15

good; and the prime factorization of 24?

Answer 16

2x2x2x3

Answer 17

excellent; now the next step has many methods that can be used; i perfer this one:

stack the factorizations one aboove the other such that like factors line up

99: 3 3 11
24: 2 2 2 3
----------------
LCM:

then drop down all the columns to fill in the LCM

99: 3 3 11
24: 2 2 2 3
----------------
LCM: 2 2 2 3 3 11 , now multiply all those values together, what do we get?

Answer 18

792?

Answer 19

792 is correct; this gives us the value that is the smallest multiple that 99 and 24 have in common

therefore: 99*n = 792
n = 792/99 , what value do we get for "n" now?

Answer 20

n = 8

Answer 21

correct. now, that is only the method I use; there are many other ways to approach this

Answer 22

oh, thanks. really appreciate it.

Answer 23

youre welcome, and good luck ;)