Question

Найдите разность НОК и НОД(30;54)

Answer 1

НОД двух чисел можно найти по алгоритму Евклида:
54 / 30 = 1 и 24 в остатке.
30 / 24 = 1 и 6 в остатке.
24 / 6 = 4 и 0 в остатке, значит, НОД = 6.

НОК = 30 * 54 / НОД = 54 * 5 = 270

270 - 6 = 264

Answer 2

Calculating the Difference Between LCM and GCD of 30 and 54

To find the difference between the least common multiple (LCM) and the greatest common divisor (GCD) of 30 and 54, we can use the following formulas:

GCD Formula: The GCD of two numbers can be calculated using the prime factorization method or by using the Euclidean algorithm.

LCM Formula: The LCM of two numbers can be calculated using the formula LCM(a, b) = (a * b) / GCD(a, b).

Let's calculate the GCD and LCM of 30 and 54 and then find their difference.

Calculating the GCD of 30 and 54

The GCD of 30 and 54 can be calculated using the prime factorization method or the Euclidean algorithm.

Using the prime factorization method: - The prime factorization of 30 is 2 * 3 * 5. - The prime factorization of 54 is 2 * 3^3.

The common prime factors are 2 and 3. Therefore, the GCD of 30 and 54 is 2 * 3 = 6.

Calculating the LCM of 30 and 54

The LCM of 30 and 54 can be calculated using the formula LCM(a, b) = (a * b) / GCD(a, b).

Using the GCD we calculated earlier: LCM(30, 54) = (30 * 54) / 6 = 270

Finding the Difference

Now, let's find the difference between the LCM and GCD: Difference = LCM - GCD = 270 - 6 = 264

Therefore, the difference between the LCM and GCD of 30 and 54 is 264.