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

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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) About Me  (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(21685) About Me  (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: 180=%28x%2Ay%29%2F12
So multiply both sides by 12
x%2Ay=2160
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
12y=2160 Plug in x=12
y=180 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:
Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 109



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: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 109


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