Наименьшее общее кратное чисел 270 и 450
How to Find the Least Common Multiple (LCM) of 270 and 450?
The LCM of two numbers is the smallest positive number that is divisible by both of them. In order to find the LCM of 270 and 450, we need to follow these steps:
- Write out the prime factorization of each number. Prime factorization means to break down a number into its prime factors. In this case, we have:
- 270 = 2 x 3 x 3 x 3 x 5
- 450 = 2 x 3 x 3 x 5 x 5
- Identify the common prime factors and their highest powers. In this case, we have 2, 3 and 5 with the highest powers being 1, 3 and 3 respectively.
- Multiply the highest powers of the common prime factors. In this case, we have (2^1)(3^3)(5^3) = 2 x 27 x 125 = 6750. Therefore, 6750 is the LCM of 270 and 450.
- Check if 6750 is divisible by both 270 and 450. In this case, 6750 is indeed divisible by both numbers, confirming our answer.
Therefore, the LCM of 270 and 450 is 6750. Hope this explanation was helpful!
