Problem solving

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I have two problems that I need help with:

1. How do I find the three digit number that satisfies the following conditions:

a. It has a factor of 3
b. It has a factor of 5
c. It has a factor of 7
d. All digits are prime.

2. If a = 2( third power) * 3 ( second power) * 5 and the GCF ( a, b) = 120 and the LCM (a,b) = 55,440, what is b?[/list][/code]
 
bware said:
I have two problems that I need help with:

1. How do I find the three digit number that satisfies the following conditions:

a. It has a factor of 3
b. It has a factor of 5
c. It has a factor of 7
d. All digits are prime.

2. If a = 2( third power) * 3 ( second power) * 5 and the GCF ( a, b) = 120 and the LCM (a,b) = 55,440, what is b?[/list][/code]
Click to expand...
Want fries with that?

1: what's lowest 3 digit number that has 3,5,7 as factors?

2: what does a equal?
 
Hello, bware!

2. If \(\displaystyle a\:=\:2^3\cdot3^2\cdot5\) and \(\displaystyle GCF(a,b)\,=\,120\) and \(\displaystyle LCM(a,b)\,=\,55,440\), what is \(\displaystyle b\)?
Click to expand...
Are you familiar with this formula? . \(\displaystyle \L\frac{a\cdot b}{GCF(a,b)}\:=\:LCM(a,b)\)

We have: .\(\displaystyle a\,=\,360\)

Therefore: .\(\displaystyle \L\frac{360b}{120}\:=\:55,440\;\;\Rightarrow\;\; b\,=\,18,480\)
 
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