The least positive integer which is a perfect square and also divisible by each of 6,12, 18 and 24?

• A. 148
• B. 144
• C. 141
• D. 152

Answer: (B)

Perfect Square : A number when written as product of prime factors , if each prime factor has even number as its power , then the number is perfect square.    Writing the given number as product of prime factors               6 = 2 x 3             12 = 2³ x 3             18 = 2 x 3²             24= 2³ x 3        LCM = 2³ x 3² = 72     But 72 is not the perfect square. But multiples of 72 are also exactly divisible by given numbers. 72 x 2 =144 is the perfect square.