What is the GCF and LCM of 36 and 45?

Oct 6, 2016

GCF is $9$ and LCM is $180$

Explanation:

A very interesting question. Well, product of GCF and LCM of any two numbers is equal to product of the two numbers, always

For finding GCF and LCM let us write them as product of prime numbers.

$36 = 2 \times 2 \times 3 \times 3$ and

$45 = 3 \times 3 \times 5$

Now we have $3 \times 3$ as the only prime common factors between them and hence, GCF is $3 \times 3 = 9$.

As $2$ and $3$ occur at the maximum two time and remaining factor $5$ occurs only once,

LCM is $2 \times 2 \times 3 \times 3 \times 5 = 180$

One may check $36 \times 45 = 9 \times 180 = 1620$