Question

Найдите НОК 36 и 77 Найдите НОД 35 и 77 И разделите НОК на НОД

Answer 1

НОК(36,77)=1
36:3           77:7
18:2           11:11
 9:3              1
 3:3
 1
НОК(35,77)=5*7=385
35:5           77:7
 7:7            11:11
 1                 1
385:1=385

Answer 2

Calculation of the Least Common Multiple (LCM) of 36 and 77

To find the Least Common Multiple (LCM) of two numbers, we need to determine the smallest number that is divisible by both numbers. In this case, we want to find the LCM of 36 and 77.

The LCM can be calculated using various methods, such as prime factorization or the division method. Let's use the division method to find the LCM of 36 and 77.

1. Start by dividing the larger number (77) by the smaller number (36): - 77 ÷ 36 = 2 remainder 5

2. Now, divide the previous divisor (36) by the remainder (5): - 36 ÷ 5 = 7 remainder 1

3. Repeat the process by dividing the previous divisor (5) by the remainder (1): - 5 ÷ 1 = 5

4. Continue dividing until we reach a remainder of 0.

Therefore, the LCM of 36 and 77 is the product of the divisors and the remainder: - LCM(36, 77) = 2 × 7 × 5 = 70

Calculation of the Greatest Common Divisor (GCD) of 35 and 77

To find the Greatest Common Divisor (GCD) of two numbers, we need to determine the largest number that divides both numbers without leaving a remainder. In this case, we want to find the GCD of 35 and 77.

The GCD can also be calculated using various methods, such as prime factorization or the Euclidean algorithm. Let's use the Euclidean algorithm to find the GCD of 35 and 77.

1. Start by dividing the larger number (77) by the smaller number (35): - 77 ÷ 35 = 2 remainder 7

2. Now, divide the previous divisor (35) by the remainder (7): - 35 ÷ 7 = 5

3. Repeat the process by dividing the previous divisor (7) by the remainder (0).

Therefore, the GCD of 35 and 77 is the remainder obtained in the previous step: - GCD(35, 77) = 7

Calculation of the Ratio of LCM to GCD

To calculate the ratio of the LCM to the GCD, we divide the LCM by the GCD.

In this case, the LCM of 36 and 77 is 70, and the GCD of 35 and 77 is 7.

Therefore, the ratio of the LCM to the GCD is: - LCM(36, 77) / GCD(35, 77) = 70 / 7 = 10

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