Question

Найдите наименьшее общее кратное чисел 27,45,90,54.И покажите как вы их нашли!

Answer 1

27=3•9
45=5•9
90=2•5•9
54=2•17
НОК(27,45,90,54)=(2•5•9)•3•17=4590

Answer 2

Finding the Least Common Multiple (LCM) of 27, 45, 90, and 54

To find the least common multiple (LCM) of the given numbers, we can use the prime factorization method. First, we'll find the prime factorization of each number, and then we'll calculate the LCM.

1. Prime Factorization of Each Number: - 27: 27 = 3 * 3 * 3 - 45: 45 = 3 * 3 * 5 - 90: 90 = 2 * 3 * 3 * 5 - 54: 54 = 2 * 3 * 3 * 3

2. Calculating the LCM: The LCM is the product of the highest powers of all prime factors involved in the numbers' prime factorizations.

LCM(27, 45, 90, 54) = 2^1 * 3^3 * 5^1 = 2 * 3^3 * 5 = 2 * 27 * 5 = 270

Therefore, the least common multiple (LCM) of 27, 45, 90, and 54 is 270.

This calculation is based on the prime factorization method, which is a commonly used approach to find the LCM of multiple numbers.