If n is a positive integer such that lcm[5n + 7, 7n + 11] = 5980, find the value of 35n^2 + 104n.

thanks in advance

Guest Jul 28, 2023

#1**-2 **

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.

The0neXWZ Aug 4, 2023