Find the smallest number that is divisible by all prime numbers between 1 and 11.
To find the smallest number that is divisible by all prime numbers between 1 and 11, we need to find the least common multiple (LCM) of these numbers.
The prime numbers between 1 and 11 are: 2, 3, 5, 7, and 11.
To find the LCM of these numbers, we can use the method of successive division to find the prime factorization of each number:
2: Prime (2)
3: Prime (3)
5: Prime (5)
7: Prime (7)
11: Prime (11)
Since all these numbers are prime, their LCM will simply be the product of these numbers:
LCM = 2 * 3 * 5 * 7 * 11 = 2310.
Therefore, the smallest number that is divisible by all prime numbers between 1 and 11 is 2310.
To find the smallest number that is divisible by all prime numbers between 1 and 11, we need to find their least common multiple (LCM).
The prime numbers between 1 and 11 are: 2, 3, 5, 7, and 11.
To find the LCM, we can list the multiples of each prime number until we find a number that is divisible by all of them.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 7: 7, 14, 21, 28, 35, ...
Multiples of 11: 11, 22, 33, 44, 55, ...
We can see that the smallest number that is divisible by all of these primes is 2 * 3 * 5 * 7 * 11 = 2310.
Therefore, the smallest number that is divisible by all prime numbers between 1 and 11 is 2310.