42, 49, 56 and 63 are all divisible by 7 and 3500 is also divisible by 7. So we need to find the smallest number we can add to 3500/7=500 to make a number that’s divisible by the LCM of 42/7, 49/7, 56/7 and 63/7, that is, the LCM of 6, 7, 8 and 9. These numbers can be written 2×3, 7, 2×4 and 3×3, so the LCM=2×3×3×4×7=504. The number to add to 500 is therefore 4.
So 504 is divisible by 6, 7, 8 and 9. Therefore 7×504=3528 is divisible by 42, 49, 56 and 63. So the least number to be added to 3500 is 28, giving us 3528.