A new school has opened with fewer than 500 students. 1/3 of the students is a whole number. So are 1/4, 1/5 and 1/7 of the students. How many students go to this school?
which number is divisible by all of
3, 4, 5, and 7?
(like finding the LCD of those)
I get 420
420
HA GOTEEM
To find the number of students at the new school, we need to determine the least common multiple (LCM) of the denominators 3, 4, 5, and 7. The LCM will give us a number that is divisible by all of these denominators, which indicates a whole number solution.
The LCM of 3, 4, 5, and 7 is 420. This means that there are 420 students at the school.
We can verify this by dividing 420 by each of the given denominators:
- 420 divided by 3 equals 140, which is a whole number.
- 420 divided by 4 equals 105, which is not a whole number.
- 420 divided by 5 equals 84, which is not a whole number.
- 420 divided by 7 equals 60, which is a whole number.
Therefore, the number of students at the new school is 420.