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

The HCF (Highest Common Factor) of two numbers 'a' and 'b' is the greatest possible number that divides both 'a' and 'b' completely.

## Answer: The third number is 47628 (2^{2} × 3^{5} × 7^{2})

Let us 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} × 3^{4} × 5

3600 = 2^{4} × 3^{2} × 5^{2}

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

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

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

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

### Therefore, the third number is 47628 (2^{2} × 3^{5} × 7^{2})

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