Question

Помогите найти НОК(12;66)

Answer 1

Разложим каждое число на простые множители:

12=2*2*3

66=2*3*11

теперь нужно выписать все множители, встречающиеся в разложении чила, которое больше, т.е.66 и ещё домножить на те, которые помимо них есть в разложении числа 12 (в данном примере это ещё одна "двойка", т.к. в разложении 66 она встречается 1 раз, а в разложении числа 12 их две)

НОК (12;66)=2**3*11*2=132

Иногда можно и проще:

просто выписываем все кратные большего числа(в данном случае это 66,132, 184 ...) и проверяем, какое из них разделится на 12). В этом примере сразу найдём 132. Но иногда это не так быстро.

Answer 2

Finding the Least Common Multiple (LCM) of 12 and 66

To find the least common multiple (LCM) of two numbers, we need to determine the smallest number that is divisible by both of them. In this case, we want to find the LCM of 12 and 66.

To find the LCM, we can use different methods such as prime factorization, listing multiples, or using the formula. Let's explore these methods:

1. Prime Factorization Method: - Prime factorize both numbers: 12 = 2^2 * 3 and 66 = 2 * 3 * 11. - Take the highest power of each prime factor: 2^2 * 3 * 11. - Multiply these prime factors together: 2^2 * 3 * 11 = 132. - Therefore, the LCM of 12 and 66 is 132.

2. Listing Multiples Method: - List the multiples of each number until you find a common multiple: - Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132... - Multiples of 66: 66, 132, 198, 264... - The first common multiple is 132. - Therefore, the LCM of 12 and 66 is 132.

3. Using the Formula Method: - Use the formula: LCM(a, b) = (a * b) / GCD(a, b), where GCD is the greatest common divisor. - Find the GCD of 12 and 66: GCD(12, 66) = 6. - Apply the formula: LCM(12, 66) = (12 * 66) / 6 = 132. - Therefore, the LCM of 12 and 66 is 132.

Based on the above methods, we can conclude that the LCM of 12 and 66 is 132.

Please note that the search results did not provide direct information about the LCM of 12 and 66. However, the methods mentioned above are commonly used to find the LCM of two numbers.