Answer: 1540
================================================
Step-by-step explanation:
To get the LCM (lowest common multiple) of 8 and 10, we can multiply the two values together to get 8*10 = 80, then we divide by the GCF (greatest common factor) which is 2 to get to the LCM of 80/2 = 40.
While 80 is a common multiple of 8 and 10, it is not the smallest such value. That would be 40. So that's why we divided by 2.
Another route we can take is to list out the multiples of 8 and 10 like so
- multiples of 8 = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...}
- multiples of 10 = {10, 20, 30, 40, 50, 60, 70, 80, ...}
as shown in bold above, the value 40 is in both lists and it is the smallest such common item.
So this tells us that the last two digits are 4 and 0 in that order.
--------------
The GCF of 30 and 75 is 15 since we can say
30 = 15*2
75 = 15*5
Note how the 2 and 5 have no other factors in common, other than 1. This helps us see how 15 is the largest shared factor. So the first two digits are 1 and 5 in that order.
Overall, the four digit code is 1540.