Question

Найдите наименьшее общее кратное чисел: 120 и 180 ОТВЕТ 360 ПОЧЕМУ??

Answer 1

120=2*2*2*3*5
180=2*2*3*3*5
НОК=2*2*2*3*3*5=360

Answer 2

Finding the Least Common Multiple (LCM) of 120 and 180

To find the least common multiple (LCM) of 120 and 180, we can use the prime factorization method. First, we'll find the prime factorization of each number, and then we'll take the highest power of all the prime factors involved.

Prime Factorization of 120: The prime factorization of 120 is 2^3 * 3 * 5.

Prime Factorization of 180: The prime factorization of 180 is 2^2 * 3^2 * 5.

To find the LCM, we take the highest power of all the prime factors involved: - The highest power of 2 is 3. - The highest power of 3 is 2. - The highest power of 5 is 1.

Therefore, the LCM of 120 and 180 is 2^3 * 3^2 * 5 = 360.

This calculation is based on the prime factorization method, which is a widely accepted approach for finding the LCM of numbers.

I hope this helps! If you have any other questions, feel free to ask.