How many numbers from 1 to 430 are divisible by 7 and 11 both?

To find: how many numbers from 1 to 430 are divisible by both 7 and 11.

If a number is divisible by both 7 and 11, it is divisible by their least common multiple (LCM). The LCM of 7 and 11 is:

LCM(7,11) = 7 × 11 = 77

The numbers divisible by 77 are of the form 77 × k, where k is an integer.

Finding the largest integer k such that 77× k ≤ 430:

​$$k = \left\lfloor \frac{430}{77} \right\rfloor = \left\lfloor 5.58 \right\rfloor = 5$$​​

The numbers divisible by 77 from 1 to 430 are:

77 × 1 = 77 , 77 × 2 = 154,77 × 3 = 231, 77 × 4 = 308, 77 × 5 = 385

Thus, There are 5 numbers between 1 and 430 that are divisible by both 7 and 11.