find the smallest perfect square divisible by 2, 3, 4 and 5.
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Solution :
The LCM of 2, 3, 4 and 5 is 60.
The least number divisible by 2, 3, 4 and 5 is their LCM, i.e. 60.
Now, 60 = 2 × 2 × 3 × 5
= 2² × 3 × 5.
Clearly, multiplying 60 by 3 × 5 = 15 makes it a perfect square.
Thus, 60 × 15 = 2² × 3² × 5².
Hence, the required least squared number is 60 × 15 = 900.
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