What is the smallest three digit number completely divisible by 12,18 and 24?
Answers
Answered by
2
it is 144 as 144/12=12
144/18=8
144/24=6
144/18=8
144/24=6
Answered by
5
first , break down each factor to its prime factors.
C.F of 12 is 3, 2, 2 = 3×2²
C.F of 18 is 3, 3, 2 = 3²×2
C.F of 24 is 3, 2, 2, 2 = 3×2³
You need to keep the max exponent for each prime factor
The lowest common factor would be :
= 3²×2³
=72
We need to find the common factor greater than 99.
So multiply it by 2 = 72×2 = 144 ∴ The smallest 3 digit no. divisible by 12, 18 and 24 is 144
C.F of 12 is 3, 2, 2 = 3×2²
C.F of 18 is 3, 3, 2 = 3²×2
C.F of 24 is 3, 2, 2, 2 = 3×2³
You need to keep the max exponent for each prime factor
The lowest common factor would be :
= 3²×2³
=72
We need to find the common factor greater than 99.
So multiply it by 2 = 72×2 = 144 ∴ The smallest 3 digit no. divisible by 12, 18 and 24 is 144
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