Find the least perfect square which is exactly division by each of the number 6,9,5 and 20

Answer: 900

Step-by-step solution

Step 1: Find prime factors of given numbers

To find a number divisible by $6$ , $9$ , $15$ , and $20$ , we first compute the least common multiple (LCM). We start by expressing each number as a product of its prime factors.

Step 2: Compute the LCM

The least common multiple is obtained by taking the highest power of each prime factor appearing in the numbers: $2^2$ , $3^2$ , and $5^1$ . Multiplying these gives $4 \times 9 \times 5 = 180$ .

Step 3: Make the LCM a perfect square

In the prime factorisation of $180$ , the prime factor $5$ does not occur in pairs. Therefore, to make $180$ a perfect square, we multiply it by $5$ , giving $180 \times 5 = 900$ , which is $30^2$ .

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