Final the least 5 digit number which is exactly
by
divisible bu
do, 25 830.
Answers
Answer:
What is the least 5-digit number which is exactly divisible by 20, 25, and 30?
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
3
What is the least 5-digit number which is exactly divisible by 20, 25, and 30?
I assume you’re asking for a positive 5-digit number. All numbers that are exactly divisible by 20, 25, and 30 are multiples of lcm(20,25,30)=300, and the smallest 5-digit multiple of 300 is ⌈10000300⌉×300 = 10200.
"Decompose each into prime factors.
20 = 2*2*5
25 = 5*5
30 = 2*3*5
Lowest common multiple is then
2*2*3*5*5 = 300
Now you need the lowest number so that
300 * N >= 10000
then
N >= 10000/300
N > 33.3…
Being N an integer, N has to be 34.
300 * 34 = 10200"
Answer:
Final the least 5 digit number which is exactly
by, 25 830. is 10200