Combinatorics by ilham akbar

There's an straight forward answer to this using a well-known theorem which Devin Ky has proven for a special case:

$Answer=\lfloor{\frac {100}{7}}\rfloor + \lfloor{\frac{100}{11}}\rfloor - \lfloor{\frac{100}{7 \times 11}}\rfloor=14+9-1=22$

Multiples of 7 less than 100: 7,14,21,..., 98 (14) Multiples of 11 less than 100: 11,22,...,99 (9) But we counted multiples of 77 twice this way, so we subtract 1 as 77 is the only number we counted twice. Thus 14 + 9 - 1 = 22.

Multiples of 7 less than 100: 7,14,21,..., 98 (14) Multiples of 11 less than 100: 11,22,...,99 (9) But we counted multiples of 77 twice this way, so we subtract 1 as 77 is the only number we counted twice. Thus 14 + 9 - 1 = 22.