What is greatest 8 digit number that can be divided by 1, 2, 3, 4, 5 and 6

Question

What is the greatest 8 digit number that can be divided by 1, 2, 3, 4, 5 and 6?

Answer 1

These numbers all go into 60. 60 goes into 100,000,000 1,666,666.7 times.

60×1666666=99999960, so we know the numbers must all go into this.

Consider 8-digit numbers higher than this divisible by:

4 and 2: 99999964, 99999968, 99999972, 99999976, 99999980, 99999984, 99999988, 99999992, 9999996

5: 99999965, 99999970, 99999975, 99999980, 99999985, 99999990, 99999995

3 and 6: 99999966, 99999972, 99999978, 99999984, 99999990, 99999996

There are no common integers so 99999960 is the largest 8-digit number.