SOLUTION: which is the samllest 3 digit number which is exactly divisible by 6,8, 12 which is the samllest 3 digit number which is exactly divisible by 8,10,12 which is the greatest 3

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Question 176346: which is the samllest 3 digit number which is exactly divisible by 6,8, 12
which is the samllest 3 digit number which is exactly divisible by 8,10,12
which is the greatest 3 digit number which is exactly divisible by 6,8, 12
which is the greatest 3 digit number which is exactly divisible by 8,10, 12
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Break down each factor to its prime factors.
6=2%2A3=2%5E1%2A3%5E1
8=2%2A2%2A2=2%5E3
12=2%2A2%2A3=2%5E2%2A3%5E1
You need to keep the max exponent for each prime factor.
The lowest common factor would be
2%5E3%2A3%5E1=8%2A3=24
We need to find the common factor greater than 99.
Multiplying by 4 would only reach 96.
Multiply by 5.
24%2A5=120
"which is the smallest 3 digit number which is exactly divisible by 6,8, 12"
120.
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8=2%2A2%2A2=2%5E3
10=2%2A5=2%5E1%2A5%5E1
12=2%2A2%2A3=2%5E2%2A3%5E1
The lowest common factor would be
2%5E3%2A3%5E1%2A5%5E1=8%2A3%2A5=120
Its also 3 digits.
"which is the samllest 3 digit number which is exactly divisible by 8,10,12"
120.
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.
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Again starting with 24 (6,8,12), the largest multiplier than keeps the product under 1000 is 41.
"which is the greatest 3 digit number which is exactly divisible by 6,8, 12"
41%2A24=984
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Again starting with 120 (8,10,12), the largest multiplier than keeps the product under 1000 is 8.
"which is the greatest 3 digit number which is exactly divisible by 6,8, 12"
120%2A8=960