Question

HCF of 3240, 3600 and a third number is 36 and their LCM is 2⁴ x 3⁵ x 5² x 7². The third number is

• A. 2⁴ x 5³ x 7²
• B. 2² x 3⁵ x 7²
• C. 2³ x 3⁵ x 7²
• D. 2⁵ x 5² x 7²

Answer 1

The Correct Option is B

The correct option is (B): 2² x 3⁵ x 7²
Explanation: The question provides that the HCF of 3240, 3600, and a third number is 36, and their LCM is \(2^4 \times 3^5 \times 5^2 \times 7^2\).
To find the third number, let's analyze:
- The prime factorizations of 3240 and 3600 are:
- 3240 = \(2^3 \times 3^4 \times 5\)
 - 3600 = \(2^4 \times 3^2 \times 5^2\)
- The HCF = 36, and the LCM is \(2^4 \times 3^5 \times 5^2 \times 7^2\).
The third number must include powers of 2, 3, 5, and 7 that are consistent with both the HCF and LCM.
After checking the options, the third number is \(2^2 \times 3^5 \times 7^2\).
Thus, the correct answer is B.