If a is the greatest common factor of 72 and 48, and if b is the greatest common factor of 108 and 144, what is the least common multiple of a and b

a = 24

b = 36

LCM = 72

612

1236

To find the least common multiple (LCM) of two numbers, you need to first find their greatest common factor (GCF) and then apply the formula LCM(a, b) = (a * b) / GCF(a, b).

Let's find the GCF of 72 and 48. One way to do this is by listing their factors and finding the largest one they have in common:

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

The largest number they have in common is 24. Therefore, the GCF of 72 and 48 is 24.

Next, let's find the GCF of 108 and 144:

Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

The largest number they have in common is 36. Therefore, the GCF of 108 and 144 is 36.

Now, we can find the LCM using the formula:

LCM(a, b) = (a * b) / GCF(a, b)
LCM(24, 36) = (24 * 36) / 12
LCM(24, 36) = 864 / 12
LCM(24, 36) = 72

So, the LCM of a and b is 72.