Find the least number which when divided by 16, 24, 32 and 40 leaves the remainder 7, 15, 23 and 31 respectively

Sure, let's solve this step by step:

1. First, we need to find the least common multiple (LCM) of the four numbers: 16, 24, 32, and 40. The LCM of these numbers is 240.

2. The problem states that when the least number is divided by any of the four numbers, the remainders are 7, 15, 23, and 31 respectively. This means that when the least number is divided by the LCM (240), the remainder should be the same.

3. However, if you subtract each of the four numbers from their respective remainders (i.e., 16-7, 24-15, 32-23, 40-31), you'll notice that they all result in 9. This means that the least number should be 9 more than a multiple of the LCM.

4. Therefore, the least number that satisfies these conditions is 240 + 9 = 249.

Sure, let's solve this step by step:

1. First, we need to find the least common multiple (LCM) of the four numbers: 16, 24, 32, and 40. The LCM of these numbers is 240.

2. The problem states that when the least number is divided by any of these four numbers, the remainders are 7, 15, 23, and 31 respectively. This means that when the least number is divided by the LCM (240), the remainder should be the same.

3. However, we notice that each of these remainders is 1 less than the divisor (16-7=9, 24-15=9, 32-23=9, 40-31=9). This means that the least number, when divided by 240, should leave a remainder of 9.

4. Therefore, the least number that satisfies these conditions is 240 + 9 = 249.