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Determine the smallest 3-digit no. that is exactly divisible by 6, 8 and 12?
- Posted:
- 3+ months ago by Priyal
- Topics:
- detail, mathematics
Details:
Responses (2)
??
The number of possibilities is small enough to write them all out and test each one.
Multiples of 12:
108
120
132
144
156
168
180
etc
Anything divisible by 12 is also divisible by 6 so we ignore that case and look for something divisible by 8.
108/8 = 13.5
120/8 = 15 <-- ANSWER
Prime factorization helps to determine the Least Common Multiple (LCM) of 6, 8 and 12 :
6 = 2 * 3
8 = 2 * 2 * 2
12 = 2 * 2 * 3
LCM (6,8,12) = 2 * 2 * 2 * 3 = 24
Hence, the smallest 3-digit number which meets the requirements must be a multiple of 24. And the smallest 3-digit multiple of 24 is
24 * 5 = 120.