Question

Найди НОК чисел с помощью разложения на множители 18, 42 , 60

Answer 1

18=2*3^2
42=7*2*3
60=5*3*4
НОК=5*3^2*4*7*2=2520

Answer 2

Finding the Least Common Multiple (LCM) of 18, 42, and 60

To find the least common multiple (LCM) of 18, 42, and 60 using their prime factorization, we can first express each number as a product of prime factors and then identify the highest power of each prime factor that appears in any of the factorizations.

- Prime Factorization of 18: - 18 = 2 * 3 * 3 - This can be expressed as 2^1 * 3^2

- Prime Factorization of 42: - 42 = 2 * 3 * 7 - This can be expressed as 2^1 * 3^1 * 7^1

- Prime Factorization of 60: - 60 = 2 * 2 * 3 * 5 - This can be expressed as 2^2 * 3^1 * 5^1

Now, we can find the LCM by taking the highest power of each prime factor that appears in any of the factorizations.

The LCM of 18, 42, and 60 is given by: LCM(18, 42, 60) = 2^2 * 3^2 * 5^1 * 7^1 = 2520

Therefore, the least common multiple (LCM) of 18, 42, and 60 is 2520. This is calculated based on the prime factorization method.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.