8. Find the least number of 5-digits which is exactly divisible by 10, 15, 20 and 25 S
Cind the greatest 3.
Answers
There are two depending on how you define least. They are 10200, or -99900.
Well first look for the LCM(least common multiple) for 20, 25, and 30.
20=2×2×5
25=5×5
30=2×3×5
All have 5 in common as a common factor, but 25 has two factors of 5 so both must be included. Thirty is the only number that has 3 as a factor, so that must be included. Twenty and 30 both have a common factor of 2, but 20 has two factors of 2 so both must be included. So that gives an LCM of 2×2×3×5×5=300
Already this can be proven before generating a five digit number because that number must be a multiple of 300. So:
300÷20=15
300÷25=12
300÷30=10
300÷300=1
As far as the least 5-digit number, there are two of them. If we are restricted to natural numbers, then the least would be 10200.
10200÷300=34
33×300=9900, so 10200 must be the least natural 5 digit number.
If instead, negative numbers are included, then -99900 is the least.
Now to test each:
10200÷20=510
10200÷25=408
10200÷30=340
10200÷300=34
-99900÷20=-4995
-99900÷25=-3996
-99900÷30=-3330
-99900÷300=-333