If you add 3 to a two digit number, you can divide it by 3, if you add 4, you can divide it by 4, if you add 5, you can divide it by 5

If you add 3 to a two digit number, you can divide it by 3, if you add 4, you can divide it by 4, if you add 5, you can divide it by 5

This number is the least common multiple of 3, 4 and 5,
3*4*5=60

The sum of the new two digit number and the original two digit number obtained after a two digit ten digit number and one digit number exchange position must be divisible by 11. Take a two digit number as an example, and explain the reason

Let B be the ten digit of the original two digit number and a be the one digit number, then the original two digit number is 10B + A, and the exchanged two digit number is 10A + B. ∵ 10B + A + (10a + b) = 10B + A + 10A + B = 11b + 11a = 11 (B + a). ∵ 11 (B + a) can be divided by 11

Try to explain that 523-521 can be divided by 120

Because 523-521 = 521 × 52-521 = 521 (52-1) = 521 × 24 = 520 × 120, 523-521 can be divided by 120