SOLUTION: I am having trouble with a question from my school text book and I have asked my teacher but I am still confused. The question is list two numbers with a HCF of 12 and a LCM of 180

Question 78172: I am having trouble with a question from my school text book and I have asked my teacher but I am still confused. The question is list two numbers with a HCF of 12 and a LCM of 180. I have asked my mum and and she doesn't get it. She checked in the awnsers fo me but that didn't help either. So can you please show me step by step workings to solve this problem. Thank you.
Found 2 solutions by checkley75, jim_thompson5910:
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
HIGHEST COMMON FACTOR EXAMPLE IS 24 & 36 HAVE A COMMON FACTOR OF 12
2*12=24 & 3*12=36
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LOWEST COMMON MULTIPLE OF 180 WOULD BE FRACTIONS WITH THE FOLLOWING NUMBERS
1/9+1/4+1/5 OR (20+45+36)/180=101/180
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
let x=1st number, y=second number
Since the LCM is the product of the 2 numbers divided by the GCF we have
LCM:
So multiply both sides by 12

So the product of the 2 numbers is 2160. We know that in order to have a GCF of 12, the lowest number is 12. So lets try x=12
Plug in x=12
Divide both sides by 12
So our second number is 180
Now lets find the GCF and the LCM between these 2 numbers:

Solved by pluggable solver: Find Greatest Common Factor

First, factorise 180 and 12:

Factors of 180: 2,2,3,3,5
Factors of 12: 2,2,3.
Highlight common factors:
180: 2,2,3,3,5
12: 2,2,3
Common factors: 2,2,3
The product of these common factors is:2*2*3=12.
This number, 12, is your greatest common factor:

Greatest Common Factor( 180, 12 ) = 12.

Now lets find the LCM

Solved by pluggable solver: Compute Least Common Multiple

LCM of two numbers can be calculated simply: calculate the product of these numbers and divide them by their greatest common factor (GCF). That's what we are going to do.

Calculate GCF of 180 and 12:

The product of 180 and 12, divided by the GCF 12, is .

So, 180 is the least common multiple of 180 and 12.

We got lucky on our first try. So it turns out that the two numbers are
12,180

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