# HCF of 3240 and 3600 and a third number is 36 and their LCM is 24 x 35 x 52 x 72. Then the third number is

HCF (Highest Common Factor) of two numbers a and b is the greatest possible number which divides both a and b exactly.

## Answer: HCF of 3240 and 3600 and a third number is 36 and their LCM is 2^{4} x 3^{5} x 5^{2} x 7^{2}. Then the third number is 47628 (2^{2} x 3^{5} x 7^{2})

Lets see how to solve it.

## Explanation:

To solve this question, we first need to express the numbers in the form of prime factors.

3240 = 2^{3} x 3^{4} x 5

3600 = 2^{4} x 3^{2} x 5^{2}

The HCF is 36 which can be expressed as 2^{2} x 3^{2} by prime factorization

The LCM in the form of prime factors is 2^{4} x 3^{5} x 5^{2} x 7^{2}

By the definition, we know that HCF is the product of the lowest power of common prime factors. This means that the third number must include the HCF, which is 2^{2} x 3^{2}.

Also, LCM is the product of the highest power of common prime factors implying that the third number must include 2^{2} x 7^{2}

Thus, the third number is 2^{2} x 3^{5} x 7^{2}.