Question

3. Знайди найменше спільне кратне чисел. а) НСК (39; 65); б) НСК (153; 204).​

Answer 1

1) 195 2)612

Пошаговое объяснение:

39|3

13|13

1|

65|5

13|13

1|

153|13

51|3

17|17

1|

204|2

102|2

51|3

17|17

1|

НСК(39;65)=13×3×5=195. НСК(153;204)=17×3×3×2×2=612

Answer 2

Finding the Least Common Multiple (LCM)

To find the least common multiple (LCM) of two numbers, we need to determine the smallest number that is divisible by both numbers.

Let's find the LCM for the given numbers:

a) LCM(39, 65) b) LCM(153, 204)

Finding the LCM of 39 and 65

To find the LCM of 39 and 65, we can use the following steps:

Step 1: Find the prime factorization of each number. - The prime factorization of 39 is 3 * 13. - The prime factorization of 65 is 5 * 13.

Step 2: Identify the highest power of each prime factor. - The highest power of 3 is 3^1. - The highest power of 5 is 5^1. - The highest power of 13 is 13^1.

Step 3: Multiply the highest powers of each prime factor. - LCM(39, 65) = 3^1 * 5^1 * 13^1 = 3 * 5 * 13 = 195.

Therefore, the least common multiple (LCM) of 39 and 65 is 195.

Finding the LCM of 153 and 204

To find the LCM of 153 and 204, we can use the same steps as above:

Step 1: Find the prime factorization of each number. - The prime factorization of 153 is 3 * 3 * 17. - The prime factorization of 204 is 2 * 2 * 3 * 17.

Step 2: Identify the highest power of each prime factor. - The highest power of 2 is 2^2. - The highest power of 3 is 3^1. - The highest power of 17 is 17^1.

Step 3: Multiply the highest powers of each prime factor. - LCM(153, 204) = 2^2 * 3^1 * 17^1 = 4 * 3 * 17 = 204.

Therefore, the least common multiple (LCM) of 153 and 204 is 204.

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