Question

НОД 280,360 НОК 280,360

Answer 1

280 = (2*2*2) * 5 * 7

360 = (2*2*2) * (3*3) * 5

НОД (280 и 360) = (2*2*2) * 5 = 40 - наибольший общий делитель

НОК (280 и 360) = (2*2*2) * (3*3) * 5 * 7 = 2520 - наименьшее общее кратное

Answer 2

To find the greatest common divisor (GCD) and the least common multiple (LCM) of two numbers, 280 and 360, we can use the prime factorization method.

Step 1: Find the prime factorization of both numbers.

Prime factorization of 280: 280 ÷ 2 = 140 140 ÷ 2 = 70 70 ÷ 2 = 35 35 ÷ 5 = 7

So, the prime factorization of 280 is 2^3 × 5 × 7.

Prime factorization of 360: 360 ÷ 2 = 180 180 ÷ 2 = 90 90 ÷ 2 = 45 45 ÷ 3 = 15 15 ÷ 3 = 5

So, the prime factorization of 360 is 2^3 × 3^2 × 5.

Step 2: Calculate the GCD.

To find the GCD, we take the product of the common prime factors with their lowest exponents:

GCD(280, 360) = 2^3 × 5 = 8 × 5 = 40.

Step 3: Calculate the LCM.

To find the LCM, we take the product of all prime factors with their highest exponents:

LCM(280, 360) = 2^3 × 3^2 × 5 = 8 × 9 × 5 = 360.

So, the GCD of 280 and 360 is 40, and the LCM is 360.