To solve this problem, we can use the relationship between the greatest common factor (GCF), least common multiple (LCM), and the two numbers. This relationship is given by the formula:
[tex]\[ \text{GCF}(a, b) \times \text{LCM}(a, b) = a \times b \][/tex]
We are given:
- The GCF is 3.
- The LCM is 180.
- One of the numbers (let's say [tex]\( a \)[/tex]) is 12.
We need to find the other number ([tex]\( b \)[/tex]).
Using the formula, we can substitute the given values:
[tex]\[ 3 \times 180 = 12 \times b \][/tex]
Let's solve for [tex]\( b \)[/tex]:
[tex]\[ 540 = 12 \times b \][/tex]
Dividing both sides by 12 to isolate [tex]\( b \)[/tex]:
[tex]\[ b = \frac{540}{12} \][/tex]
[tex]\[ b = 45 \][/tex]
Thus, the other number is:
(b) 45
