Question

What is the least positive integer k for which 15k is the cube of a number?

Answer 1

first write 15 as a product of primes

Answer 2

3 times 5

Answer 3

good. now can you see what 'k' must be in order to get 15k to be a cube?

Answer 4

you have:

15k = 3 * 5 * k

Answer 5

and then ...

Answer 6

ok - first just concentrate on the '3'. what must you multiply '3' by in order to get a perfect cube?

Answer 7

3 times 3 times 3

Answer 8

perfect!

can you what to do now?

Answer 9

*you see

Answer 10

225?

Answer 11

5 timse 5 times 5?

Answer 12

5^3 = 125

Answer 13

so, to make '3' into a cube (smallest cube) - you need to multiply it by 3^2
similarly, to make '5' into a cube - you need to multiply it by 5^2

Answer 14

OH I GET IT NOW

Answer 15

u need to cube 15, but since theires oalready 1 15, you need two more, or 15 squared which is 125

Answer 16

you must remember to first express the number as a product of its prime factors

Answer 17

e.g. what is the smallest cube for 45k ?

Answer 18

it is not 45^3

Answer 19

3375?

Answer 20

45 = 3^2 * 5

so smallest cube would be achieved by multiplying 45 by 3 * 5^2

Answer 21

?

Answer 22

yes 3375
you should now be able to work out what 'k' should be equal to

Answer 23

oh
i did its 225

Answer 24

perfect! well done!

Answer 25

so basically cube all the factors and times them?

Answer 26

correct :)

Answer 27

yay ty

Answer 28

yw :)