Find the smallest number which when successively divided

The greatest number that will divide 398, 437 and 5425 leaving 7, 12 and 2 as remainders, respectively, is:

Which of the following pairs of non-zero values of p and q make 6-digit number 674pq0 divisible by both 3 and 11?

What are the last two digits of 56²⁸³ x 141²⁸³ × 125²⁵⁴?

A five-digit number 2A78B, is divisible by 55. What is the difference between the maximum and minimum possible value of (A-B)?

Find the largest 4-digit number that is exactly divisible by 27 and 45.

Find the least 4-digit number which is when divided by 16, 20, and 24 leaves a remainder of 9 in each case.

What is the remainder when 123456 is divided by 9?

What is the smallest perfect square that is divisible by each of 42, 48 and 60?

Find the smallest 4-digit number which when divided by 10, 15, 20, 25, 30 leaves remainder 9.

Find the smallest positive integer n such that 6n + 5 is divisible by 7.