Question : Let $x$ be the least number divisible by 16, 24, 30, 36, and 45, also $x$ is also a perfect square. What is the remainder when $x$ is divided by 123?
Option 1: 100
Option 2: 40
Option 3: 103
Option 4: 33
Correct Answer: 33
Solution :
Given: Let $x$ be the least number divisible by 16, 24, 30, 36, and 45, also $x$ is a perfect square.
LCM of 16, 24, 30, 36, and 45 = 2
4
× 3
2
× 5 = 720
The number is not a perfect square.
⇒ 2
4
× 3
2
× 5
2
= 720 × 5 = 3600, which is a perfect square.
When the number 3600 is divided by 123, the remainder is 33 i.e. $x$ = 33
Hence, the correct answer is 33.
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