A number between 61 and 107 that is a multiple of 3,8, and 12

The number that those factors all have in common is 72.

3 x 24 = 72

8 x 9 = 72

12 x 6 = 72.

If it is a multiple of 3,8 and 12 the least common multiple is found using prime factorization ...

3=3, 8=2*2*2, 12=2*2*3

The LCM is the product of the highest occurring primes for the three numbers ...

LCM=2*2*2*3=24

So the number must be a multiple of 24 and to be between 61 and 107 we can say:

61<24n<107 divide all terms by 24

2.5
The possible integer values for n are 3 and 4

And since the numbers are 24n, there are two such numbers which fall in between 61 and 107 and they are

24*3 and 24*4

72 and 96