Number Theory
# Prime Factorization and Divisors

What is the smallest positive integer divisible by each of 10, 20, and 30?

What is \(a \times b \, ?\)

**Hint:** \(5040 = 7! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7.\)

What is the smallest number that is divisible by 1, 2, 3, 4, 5 and 6?

Which of these statements are true?

I. Even numbers are never divisible by odd numbers.

II. Odd numbers are never divisible by even numbers.

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