If n is a positive integer such that lcm[5n + 7, 7n + 11] = 5980, find the value of 35n^2 + 104n.
thanks in advance
-649 The LCM of two integers is the smallest positive integer that is a multiple of both integers. So, we know that 5980 is the LCM of 5n + 7 and 7n + 11.
We can factor out 7 from 7n + 11 to get 7(n + 1). We can also factor out 5 from 5n + 7 to get 5(n + 1). So, we can write 5n + 7 and 7n + 11 as 7(n + 1) and 5(n + 1), respectively.
The LCM of 7(n + 1) and 5(n + 1) is 35(n + 1). So, we know that 5980 = 35(n + 1).
Dividing both sides by 35, we get n + 1 = 170.
Subtracting 1 from both sides, we get n = 169.
Plugging this value of n into 35n^2 + 104n, we get 35 * 169^2 + 104 * 169 = 5980 * 169 = 997,460.
Therefore, the value of 35n^2 + 104n is 997,460.
