Question

Во сколько раз наибольший общий делитель числа 210 и наибольшего чётного двузначного числа меньше их наименьшего общего кратного?

Answer 1

Наибольшее чётное двузначное число - 98=3*4*7

210 = 2*3*5*7

Набольший общий делитель 7

Наименьшее общее кратное 3*7 = 21

Answer 2

Calculation of the Greatest Common Divisor (GCD) and Least Common Multiple (LCM)

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. The least common multiple (LCM) is the smallest multiple that is divisible by both numbers.

Let's calculate the GCD of 210 and the largest even two-digit number that is smaller than their LCM.

The largest even two-digit number is 98.

To find the GCD, we can use the Euclidean algorithm, which involves finding the remainder when dividing the larger number by the smaller number, then dividing the smaller number by the remainder. This process is repeated until the remainder is zero.

Here are the steps to calculate the GCD:

1. Divide 210 by 98: 210 ÷ 98 = 2 with a remainder of 14. 2. Divide 98 by 14: 98 ÷ 14 = 7 with a remainder of 0.

Since the remainder is now zero, we have found the GCD. The GCD of 210 and 98 is 14.

Now, let's calculate the LCM of 210 and 98. The LCM can be found by dividing the product of the two numbers by their GCD.

The product of 210 and 98 is 20,580.

To find the LCM, we divide the product by the GCD:

20,580 ÷ 14 = 1,470.

Therefore, the LCM of 210 and 98 is 1,470.

Conclusion

The GCD of 210 and 98 is 14, and the LCM of 210 and 98 is 1,470.