Question

НОК(51;17) НОК(16;48)

Answer 1

НОК(51, 17) =3 • 17 = 51;
17 = 1 • 17
51 = 3 • 17
НОК(16,48) = 2^4 • 3 = 16 • 3 = 48;
16 = 2 • 2 • 2 • 2
48 = 2• 2 • 2 • 2 • 3

Answer 2

Calculation of the least common multiple (LCM) of 51 and 17

To calculate the least common multiple (LCM) of two numbers, we need to find the smallest number that is divisible by both numbers without leaving a remainder.

The LCM of 51 and 17 can be calculated using various methods, such as prime factorization or listing multiples. Let's use the prime factorization method.

Prime factorization of 51: - 51 can be factored as 3 * 17.

Prime factorization of 17: - 17 is a prime number, so it cannot be factored further.

To find the LCM, we take the highest power of each prime factor that appears in either number: - The highest power of 3 is 1. - The highest power of 17 is 1.

Therefore, the LCM of 51 and 17 is 3 * 17 = 51.

Calculation of the least common multiple (LCM) of 16 and 48

Using the same method, let's calculate the LCM of 16 and 48.

Prime factorization of 16: - 16 can be factored as 2 * 2 * 2 * 2.

Prime factorization of 48: - 48 can be factored as 2 * 2 * 2 * 2 * 3.

To find the LCM, we take the highest power of each prime factor that appears in either number: - The highest power of 2 is 4. - The highest power of 3 is 1.

Therefore, the LCM of 16 and 48 is 2 * 2 * 2 * 2 * 3 = 48.

So, the LCM of (51, 17) is 51, and the LCM of (16, 48) is 48.