Question

The LCM of 8, 9 and 25 is

• A. 420
• B. 1139
• C. 216
• D. (D) 1800

Hint:

When numbers are co-prime (no common prime factors), their LCM is simply their product. Always check prime overlap first—it saves time in exams.

Answer 1

The Correct Option is D

Concept: The Least Common Multiple (LCM) of given numbers is the smallest positive integer that is exactly divisible by each of them. The most systematic method to find LCM is prime factorization, where we take the highest power of each prime factor present in the numbers.

Step 1: Prime factorization of each number.
• \(8 = 2 \times 2 \times 2 = 2^3\)
• \(9 = 3 \times 3 = 3^2\)
• \(25 = 5 \times 5 = 5^2\)

Step 2: Identify all prime factors. The numbers involve primes \(2, 3,\) and \(5\). There is no overlap between them, so all highest powers must be included.

Step 3: Compute the LCM. \[ \text{LCM} = 2^3 \times 3^2 \times 5^2 \] \[ \text{LCM} = 8 \times 9 \times 25 \] \[ \text{LCM} = 72 \times 25 = 1800 \] Final Answer: \[ \boxed{1800} \]