Question
Download Solution PDFDetermine the smallest 3-digit number which is exactly divisible by 6 and 12 ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
We need to determine the smallest 3-digit number which is exactly divisible by both 6 and 12.
Formula Used:
A number divisible by both 6 and 12 must be divisible by their Least Common Multiple (LCM).
LCM of 6 and 12 is used to find the smallest 3-digit number divisible by both.
Calculation:
Find LCM of 6 and 12.
Prime factorization of 6 = 2 × 3
Prime factorization of 12 = 22 × 3
LCM = Highest powers of all prime factors = 22 × 3 = 12
Smallest 3-digit number = 100
Divide 100 by 12:
100 ÷ 12 = 8 (quotient) and remainder = 4
Next multiple of 12 = 100 + (12 - remainder)
⇒ 100 + (12 - 4) = 100 + 8 = 108
Smallest 3-digit number divisible by 12 = 108
The smallest 3-digit number divisible by 6 and 12 is 108.
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