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

Answer: (B)

22 x 35 x 72

Answer 2

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.