What are the largest 4-digit and the smallest 3-digit numbers divisible by 6, 15, 21 and 24?Options 9235, 420 9980, 840 9240, 840 9999, 999

To find the largest 4-digit number divisible by 6, 15, 21, and 24, we need to find the least common multiple (LCM) of these numbers. The LCM of 6, 15, 21, and 24 is 840.

Now, to find the largest 4-digit number divisible by 840, we divide the largest 4-digit number, 9999, by 840. The quotient is 11 and the remainder is 879. So, we subtract 879 from 9999 to get the largest 4-digit number divisible by 840, which is 9120.

To find the smallest 3-digit number divisible by 840, we divide the smallest 3-digit number, 100, by 840. The quotient is 0 and the remainder is 100. So, we add 840 - 100 to get the smallest 3-digit number divisible by 840, which is 840.

So, the largest 4-digit number and the smallest 3-digit number divisible by 6, 15, 21, and 24 are 9120 and 840, respectively. However, none of the options provided match these numbers.