Directions: What is the smallest number, greater than zero, that is divisible by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10?

### Hint

### Hint

Does the number have to be even or odd? How do you know?

What digit must be in the ones place? How do you know?

The sum of the digits must be equal to a multiple of what number?

What digit must be in the ones place? How do you know?

The sum of the digits must be equal to a multiple of what number?

### Answer

### Answer

2,520

Source: Brian Lack

Rather than being divisible by various numbers, what if there is a remainder?

For example:

Suppose you divide a number by 2 and the remainder is 1.

Suppose, further, that when you divide this number by 3, 4, 5, 6, and 7, the remainder in each case is 1.

What is the smallest positive number that satisfies the constraints above?

Rather than being divisible by various numbers,what if there is a remainder?

For example:

Suppose you divide a number by 2 and the remainder is q.

Suppose,further,that when you divide this number by 3, 4, 5,6, and 7, the remainder in each case is 1.

What is the smallest positive number that satisfies the constraints above?