Which smallest number of 5 digits is divisible by65
Answers
Answer:
Check
Explanation:
Part 1: GCF
To solve for GCF, we find the prime factorization of both numbers and see which common prime factors it has and then we multiply the two factors together.
65 = 5 * 13
80 = 5 * 2^4
They both share one 5, meaning the GCF is 5.
Part 2: LCM
To solve for the LCM, there is a formula, stating that the LCM is one number divided by the GCF, and then multiplied by the other number.
LCM(65, 80) = 65/5*80
LCM(65, 80) = 13*80
LCM(65, 80) = 1040
If we know that the LCM is 1040, we just need to find a number that when multiplied by 1040 gives a 5 digit number.
Part 3: Finding the 5 Digit Number
We know that a possible five digit number that would be a common multiple of 65 and 80 would be 10400, the product of the LCM and 10. To make sure that there is none lower than 10400, we must subtract 1040 from 10400.
10400 - 1040 = 9360
Therefore, the smallest 5 digit number that is divisible by 65 and 80 is 10400.