НОК(12, 50)

To find the least common multiple (LCM) of 12 and 50, you can use the prime factorization method or the division method.

Using the prime factorization method:

1. Prime factorize each number:

   • 12 = 2^2 * 3
   • 50 = 2 * 5^2

2. Write down all the prime factors with their highest exponents from both numbers:

   • 2^2 * 3 * 5^2

3. Multiply these prime factors together: 2^2 * 3 * 5^2 = 4 * 3 * 25 = 300

Therefore, the least common multiple (LCM) of 12 and 50 is 300.

Using the division method:

1. Start by writing out the numbers 12 and 50.

2. Divide each number by prime factors (starting from 2) until you cannot divide anymore:

   • For 12: Divide by 2, resulting in 6. Divide by 2 again, resulting in 3.
   • For 50: Divide by 2, resulting in 25.

3. Write down all the divisors and the remaining numbers:

   • Divisors: 2, 2, 3, 5, 25

4. Multiply all the divisors together: 2 * 2 * 3 * 5 * 25 = 300

Again, the least common multiple (LCM) of 12 and 50 is 300.