How many Positive integers are between 200-500 that are divisible by the integers 4,6,10,12?
Do you mean GCM??? There is no such thing as an HCM well there is butter not in mathmatical terms..
Thanks,
Erika
but*
wow...
To find the number of positive integers between 200 and 500 that are divisible by the integers 4, 6, 10, and 12, we can use the concept of least common multiple (LCM).
First, let's find the LCM of the given numbers, which are 4, 6, 10, and 12.
Prime factorization:
4 = 2^2
6 = 2 * 3
10 = 2 * 5
12 = 2^2 * 3
LCM = 2^2 * 3 * 5 = 60
The LCM of 4, 6, 10, and 12 is 60.
Now, we need to find the number of positive integers between 200 and 500 that are divisible by 60.
To do this, we can divide 500 by 60 and round down to the nearest whole number. This gives us 8.
Similarly, we divide 200 by 60 and round up to the nearest whole number. This gives us 4.
Finally, we subtract the rounded-up value from the rounded-down value (8 - 4) to get 4.
Therefore, there are 4 positive integers between 200 and 500 that are divisible by 4, 6, 10, and 12.
The first number after 200 which meets your conditions is 240.
After that it will be every 240 + HCM of 4,6,10 and 12
which is 60
So the numbers would be 240, 300, 360, 420, and 480