Mohendersrivastavaidn
Answered

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2. The greatest common factor and least common multiple of two numbers are 3 and 180, respectively. One of the numbers is 12. What is the other number?

A. 54
B. 45
C. 40
D. 50

Sagot :

GinnyAnsweridn
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
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