Question

Найдите НОК:16 и 246 и 921 и 3582 и 12350 и 125225 и 75156 и 336564 и 564

Answer 1

48

18
105

246

250
225
4368
564

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Answer 2

Finding the Least Common Multiple (LCM) of Numbers

To find the least common multiple (LCM) of a set of numbers, we can use the prime factorization method. First, we find the prime factorization of each number, and then we take the highest power of all the prime factors present in the factorizations. Let's calculate the LCM for the given numbers: 16, 246, 921, 3582, 12350, 125225, 75156, 336564, and 564.

1. Prime Factorization of Each Number: - 16: 16 = 2^4 - 246: 246 = 2 * 3 * 41 - 921: 921 = 3^2 * 103 - 3582: 3582 = 2 * 29 * 31 - 12350: 12350 = 2 * 5^2 * 19^2 - 125225: 125225 = 5^2 * 7^2 * 13^2 - 75156: 75156 = 2^2 * 3 * 19 * 659 - 336564: 336564 = 2^2 * 3 * 28047 - 564: 564 = 2^2 * 3 * 47

2. Highest Powers of Prime Factors: - 2^4, 3^2, 5^2, 7^2, 13^2, 19^2, 29, 31, 41, 47, 103, 659, 28047

3. Calculating the LCM: - LCM = 2^4 * 3^2 * 5^2 * 7^2 * 13^2 * 19^2 * 29 * 31 * 41 * 47 * 103 * 659 * 28047 - LCM = 122386894400

Therefore, the least common multiple (LCM) of the given numbers: 16, 246, 921, 3582, 12350, 125225, 75156, 336564, and 564 is 122386894400.