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Topics in Quantitative Aptitude
Find the LCM (Least Common Multiple) of 12 and 18.
Correct Answer:
C. 36
EXPLANATION
This question asks us to find the smallest positive number that is divisible by both 12 and 18.
Step 1: Find Prime Factorization of Both Numbers
Break down each number into its prime factors.
\[12 = 2^2 \times 3\]
\[18 = 2 \times 3^2\]
Step 2: Identify Highest Powers of All Prime Factors
The LCM uses the highest power of each prime factor that appears.
\[\text{LCM} = 2^{\text{max}(2,1)} \times 3^{\text{max}(1,2)} = 2^2 \times 3^2\]
Step 3: Calculate the LCM
Multiply the highest powers together.
\[2^2 \times 3^2 = 4 \times 9 = 36\]
The LCM of 12 and 18 is 36, which is the smallest number divisible by both numbers.
