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Question

What is the smallest square number which is divisible by 2,4,5,6 and 9?


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Solution

Step 1: Find the LCM of given numbers.

Apply the prime factorization method to calculate the lcm of the given numbers.

2=1×2

4=1×2×2

5=1×5

6=1×2×3

9=1×3×3

So, the required lcm is:

LCM2,4,5,6,9=2×2×3×3×5LCM2,4,5,6,9=180

Step 2: Find the least square number we complete the pairs.

180=2×2×3×3×5

We just needed one 5 to complete the pair.

We get least square number is:

2×2×3×3×5×5=900

Hence, the required least square number is 900.


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