Find the least possible 4 digit number, which when divided by 10, 12, 16 and 20 leaves the remainder 27.

Sure, here is the step by step solution:

Step 1: Find the least common multiple (LCM) of the divisors (10, 12, 16, 20). The LCM of these numbers is 240.

Step 2: The least 4 digit number is 1000. Divide 1000 by 240, the remainder is 160.

Step 3: Subtract the remainder from the LCM. 240 - 160 = 80.

Step 4: Add this difference to the least 4 digit number. 1000 + 80 = 1080. This is the smallest 4 digit number divisible by 10, 12, 16, and 20.

Step 5: But we need the number to leave a remainder of 27 when divided by these numbers. So, add 27 to the number we found in step 4. 1080 + 27 = 1107.

So, the least possible 4 digit number, which when divided by 10, 12, 16 and 20 leaves the remainder 27 is 1107.