Rafael must choose a number between 55 and 101 that is a multiple of. 4,6, and 9
. write all the numbers that he could choose. if there is more than one number, separate them with commas.

If it is a multiple of 4, 6, and 9 it must be a multiple of the least common multiple.  The LCM is the product of highest occurring primes among the numbers prime factorization...

4=2*2, 6=2*3, 9=3*3  so the LCM is 2*2*3*3=36

Now we want to know the multiples of 36 between 55 and 101 so

55<36n<101  divide all terms by 36

1.52<n<2.8  and since n must be an integer n=2 so the only number that is a multiple of 4,6, and 9 between 55 and 101 is:

2*36=72