Question

НОК(9,6) НОК(12,15) НОК (20,25)

Answer 1

Чтобы найти НОК нескольких чисел, нужно разложить эти числа на простые множители и найти произведение всех простых множителей,взятых с наибольшим показателем степени.

9 = (3*3)

6 = 2 * 3

НОК (9 и 6) = 2 * (3*3) = 18 - наименьшее общее кратное

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12 = (2*2) * 3

15 = 3 * 5

НОК (12 и 15) = (2*2) * 3 * 5 = 60 - наименьшее общее кратное

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20 = (2*2) * 5

25 = (5*5)

НОК (20 и 25) = (2*2) * (5*5) = 100 - наименьшее общее кратное

Answer 2

To find the least common multiple (LCM) of two or more numbers, you can use the formula:

LCM(a, b) = (a * b) / GCD(a, b)

where GCD(a, b) represents the greatest common divisor of 'a' and 'b'. Since you provided three pairs of numbers, let's find the LCM for each pair:

1. LCM(9, 6): To find the LCM of 9 and 6, first, we need to find their GCD. Factors of 9: 1, 3, 9 Factors of 6: 1, 2, 3, 6 The greatest common divisor (GCD) of 9 and 6 is 3.

Now, use the LCM formula: LCM(9, 6) = (9 * 6) / 3 = 54 / 3 = 18

So, LCM(9, 6) = 18

2. LCM(12, 15): To find the LCM of 12 and 15, first, we need to find their GCD. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 15: 1, 3, 5, 15 The greatest common divisor (GCD) of 12 and 15 is 3.

Now, use the LCM formula: LCM(12, 15) = (12 * 15) / 3 = 180 / 3 = 60

So, LCM(12, 15) = 60

3. LCM(20, 25): To find the LCM of 20 and 25, first, we need to find their GCD. Factors of 20: 1, 2, 4, 5, 10, 20 Factors of 25: 1, 5, 25 The greatest common divisor (GCD) of 20 and 25 is 5.

Now, use the LCM formula: LCM(20, 25) = (20 * 25) / 5 = 500 / 5 = 100

So, LCM(20, 25) = 100

To summarize:

• LCM(9, 6) = 18
• LCM(12, 15) = 60
• LCM(20, 25) = 100