Since we want a to be as large as possible, we want b to be as small as possible.  The lowest possible value of b, then, is 4.  If b is 4, then we can solve for a by setting up the equation:

4(a) = 96

96/4 = 24

The least comon multiple is the lowest multiple of all three numbers. 160 is 32x5, 16x10, and 8x20.

To find the least common multiple of two numbers, if they are both prime, simply multiply the numbers.

Thus we get that 

We could also write out the multiples of each number and see what numbers they have in common. The least common multiple will be the common number that appears first in both sets.

To find the lowest common multiply, we need to find the smallest value which is a factor of each of the three numbers. We know it has to be even from the factor of two. If we look at the value , the lowest multiple of that number is  Since the other two values are also divisible by this number, that is the lowest common multiple.

If you divide the answer choices by 4, 5, and 6, 120 is the only choice that divides evenly by all three numbers.

The greatest common factor is the largest integer that divides without remainder into a set of integers. In this case, 1 and 7 are both common factors, but 7 is the greatest common factor.

The greatest common factor is the largest factor that the given numbers have in common. 5 is a common factor, but it is not the greatest one; 11 and 20 are not common factors to the given numbers; however, 55 is a common factor of the given three numbers and is the greatest one at that.

The greatest common factor can most easily be found by plugging in answers from your answer choices, a good strategy with these types of problems is to simply guess and check using your largest answer, in this case, we see that 30 is immediately the GCF for these three numbers

GCF=greatest common factor. First find the factors of each number. So the factors for each number are

36: 1, 36, 2, 18, 3, 12, 4, 9, 6

64: 1, 64, 2, 32, 4, 16

144:1, 144, 2, 72, 3, 48, 4, 36, 6, 24, 8, 18, 9, 16, 12.

1, 2, and 4 are the only factors that are common to 36, 64, and 144. Since 4 is the greatest of these factors, it is the correct answer. 

We can find the greatest common factor of a series of numbers by performing the prime factorization of each number. The greatest common factor will be the product of the combinations of prime factors that each number has in common. 36 can be factorized to 2² * 3².108 can be factorized to 2² * 3³.  180 can be factorized to 3² * 2² * 5. The greatest common prime factorization is 2² * 3², the product of which is 36. So 36 is the greatest common factor. Remember that 2² * 3³ = 2² * 3² * 3.