Question

Найти НОД и НОК 324 и 180 84 и 96 25 и 10 190 и 98

Answer 1

НОД(324;180)=2×2×3×3=36
НОК(324;180)=2×2×3×3×3×3×5=1620
324=2×2×3×3×3×3
180=2×2×3×3×5

НОД(84;96)=2×2×3=12
НОК(84;96)=2×2×2×2×2×3×7=672
84=2×2×3×7
96=2×2×2×2×2×3

НОД(25;10)=5
НОК(25;10)=5×5×2=50
25=5×5
10=2×5

НОД(190;98)=2
НОК(190;98)=2×5×19×7×7=9310
190=2×5×19
98=2×7×7

Answer 2

Finding the Greatest Common Divisor (GCD) and Least Common Multiple (LCM)

To find the GCD and LCM of the given numbers, we can calculate them step by step.

1. Finding the GCD of 324 and 180: - The GCD of 324 and 180 is 36. - The GCD can be calculated using the prime factorization method or the Euclidean algorithm. - The prime factorization of 324 is 2^2 * 3^4 and the prime factorization of 180 is 2^2 * 3^2 * 5. - Using the prime factorization method, the GCD is the product of the common prime factors raised to the lowest powers, which is 2^2 * 3^2 = 36.

2. Finding the GCD of 84 and 96: - The GCD of 84 and 96 is 12. - The prime factorization of 84 is 2^2 * 3 * 7 and the prime factorization of 96 is 2^5 * 3. - Using the prime factorization method, the GCD is the product of the common prime factors raised to the lowest powers, which is 2^2 * 3 = 12.

3. Finding the GCD of 25 and 10: - The GCD of 25 and 10 is 5. - The GCD can be calculated using the prime factorization method or the Euclidean algorithm. - The prime factorization of 25 is 5^2 and the prime factorization of 10 is 2 * 5. - Using the prime factorization method, the GCD is the product of the common prime factors raised to the lowest powers, which is 5.

4. Finding the LCM of 324 and 180: - The LCM of 324 and 180 is 1620. - The LCM can be calculated using the prime factorization method or by using the formula LCM(a, b) = (a * b) / GCD(a, b). - Using the formula, LCM(324, 180) = (324 * 180) / 36 = 1620.

5. Finding the LCM of 84 and 96: - The LCM of 84 and 96 is 336. - The LCM can be calculated using the prime factorization method or by using the formula LCM(a, b) = (a * b) / GCD(a, b). - Using the formula, LCM(84, 96) = (84 * 96) / 12 = 336.

6. Finding the LCM of 25 and 10: - The LCM of 25 and 10 is 50. - The LCM can be calculated using the prime factorization method or by using the formula LCM(a, b) = (a * b) / GCD(a, b). - Using the formula, LCM(25, 10) = (25 * 10) / 5 = 50.

In summary, the GCD and LCM of the given numbers are as follows: - GCD(324, 180) = 36, GCD(84, 96) = 12, GCD(25, 10) = 5 - LCM(324, 180) = 1620, LCM(84, 96) = 336, LCM(25, 10) = 50