Question

Во сколько раз НОД числа 210 и наибольшего четного двузначного числа меньше их НОК

Answer 1

 98- наибольшее четное двузначное число

Простые множители числа 210:  2,5,3,7,1

простые множители числа 98:   2,7,7,1;

общим множителем являются числа 2 и 7,а их 2х7=14,тогда НОД(210,98)=14

НОК(210,98)= 2х5х3х7х7=1470

1470:14=105

Ответ: в 105 раз НОД(210,98)<НОК(210,98) 

Answer 2

Calculation of the GCD and LCM

To find the ratio between the greatest common divisor (GCD) of two numbers and their least common multiple (LCM), we first need to calculate the GCD and LCM of the given numbers.

The given numbers are 210 and the largest even two-digit number.

Let's calculate the GCD and LCM step by step.

1. GCD Calculation: The GCD is the largest positive integer that divides both numbers without leaving a remainder.

The prime factorization of 210 is 2 * 3 * 5 * 7. The prime factorization of the largest even two-digit number (98) is 2 * 7 * 7.

To calculate the GCD, we take the highest power of each common prime factor. In this case, the highest power of 2 is 2, the highest power of 3 is 0, the highest power of 5 is 0, and the highest power of 7 is 1.

Therefore, the GCD of 210 and 98 is 2 * 7 = 14.

2. LCM Calculation: The LCM is the smallest positive integer that is divisible by both numbers.

To calculate the LCM, we take the highest power of each prime factor from both numbers. In this case, the highest power of 2 is 1, the highest power of 3 is 0, the highest power of 5 is 0, and the highest power of 7 is 2.

Therefore, the LCM of 210 and 98 is 2 * 7 * 7 = 98.

Ratio between GCD and LCM

Now that we have calculated the GCD and LCM, we can find the ratio between them.

The ratio between the GCD and LCM is given by the formula:

Ratio = GCD / LCM

Substituting the values we calculated earlier:

Ratio = 14 / 98

Simplifying the ratio:

Ratio = 1 / 7

Therefore, the ratio between the GCD of 210 and the largest even two-digit number and their LCM is 1:7.

Please note that the specific value of the largest even two-digit number was not provided, so we cannot provide an exact numerical answer. However, the ratio between the GCD and LCM remains the same regardless of the specific value of the largest even two-digit number.

I hope this helps! Let me know if you have any further questions.