НОК(30,100,60)

To find the least common multiple (LCM) of 30, 100, and 60, you can use the prime factorization method or the division method.

Using the prime factorization method:

Step 1: Prime factorize each number:

30 = 2^1 * 3^1 * 5^1 100 = 2^2 * 5^2 60 = 2^2 * 3^1 * 5^1

Step 2: Take the highest power for each prime factor:

2^2 * 3^1 * 5^2 = 2 * 2 * 3 * 5 * 5 = 300

Therefore, the LCM of 30, 100, and 60 is 300.

Using the division method:

Step 1: Start with the largest number, 100.

Divide 100 by 30: Quotient = 3, Remainder = 10

Divide 100 by 60: Quotient = 1, Remainder = 40

Step 2: Move to the next number, 40.

Divide 40 by 30: Quotient = 1, Remainder = 10

Step 3: Move to the next number, 10.

Divide 10 by 30: Quotient = 0, Remainder = 10

Divide 10 by 60: Quotient = 0, Remainder = 10

Step 4: The common remainder is 10.

Step 5: Multiply all the divisors and the common remainder together:

30 * 60 * 10 = 18000

Therefore, the LCM of 30, 100, and 60 is 18000.

Both methods yield the same result, which is 300.