What is the least number which when divided 6, 7and 8 leaves 1, 2, 3 as the remainders respectively.Options173   168150163

The least number which when divided by 6, 7, and 8 leaves 1, 2, and 3 as the remainders respectively is 173.

Here's how you can find it:

Step 1: Since the numbers 6, 7, and 8 are co-prime, you can find the least number divisible by all these numbers by simply multiplying them together. This gives you 336.

Step 2: Now, you need to find a number which gives the remainders 1, 2, and 3 when divided by 6, 7, and 8 respectively. This means the number you're looking for is of the form 336k + r, where k is a positive integer and r is the remainder.

Step 3: By trying different values of k, you'll find that when k=1, the remainder r is 173. This means the least number which satisfies the conditions is 173.