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Try this beautiful problem from Algebra based on the ratio of LCM & GCF from AMC-8, 2013.

## Ratio of LCM & GCF | AMC-8, 2013 | Problem 10

What is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594?

• 310
• 330
• 360

### Key Concepts

Algebra

Ratio

LCM & GCF

But try the problem first…

Answer:$330$

Source

AMC-8, 2013 problem 10

Challenges and Thrills in Pre College Mathematics

## Try with Hints

First hint

We have to find out the ratio of least common multiple and greatest common factor of 180 and 594. So at first, we have to find out prime factors of 180 & 594. Now…….

$180=3^2\times 5 \times 2^2$

$594=3^3 \times 11 \times 2$

Can you now finish the problem ……….

Second Hint

Now lcm of two numbers i.e multiplications of the greatest power of all the numbers

Therefore LCM of 180 & 594=$3^3\times2^2 \times 11 \times 5$=$5940$

For the GCF of 180 and 594, multiplications of the least power of all of the numbers i.e $3^2\times 2$=$18$

can you finish the problem……..

Final Step

Therefore the ratio of Lcm & gcf of 180 and 594 =$\frac{5940}{18}$=$330$