Question : Find the least number which when divided by 12, 18, 24, and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Option 1: 366
Option 2: 364
Option 3: 384
Option 4: 634
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Correct Answer: 364
Solution :
Given: The least number which when divided by 12, 18, 24, and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
The Least Common Multiple (LCM) of such numbers is the least number that may be divided by multiple numbers.
The least number that is divisible by 12, 18, 24, and 30 = LCM of 12, 18, 24, and 30 = 360.
⇒ The least number when divided by 12, 18, 24, and 30, leaves a remainder of 4 = 360 + 4 = 364.
Also, 364 is divisible by 7.
Hence, the correct answer is 364.
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