Question

Помогите Найдите: НОК (34;64) НОК (99;88). НОК (25;75;120) НОК (17;34;51)

Answer 1

Ответ:

НОК(34;64) = 2⁶•17 = 1088

НОК(99;88) = 3²•11•2³ = 792

НОК(25;75;120) = 2³•3•5² = 600

НОК(17;34;51) = 3•17•2 = 102

Answer 2

Finding the Least Common Multiple (LCM)

To find the least common multiple (LCM) of two or more numbers, we need to determine the smallest number that is divisible by all the given numbers. Let's find the LCM for the given numbers:

1. LCM(34, 64): - We can use the prime factorization method to find the LCM. - Prime factorization of 34: 2 * 17 - Prime factorization of 64: 2^6 - The LCM is the product of the highest powers of all prime factors: 2^6 * 17 = 1088.

2. LCM(99, 88): - Prime factorization of 99: 3^2 * 11 - Prime factorization of 88: 2^3 * 11 - The LCM is the product of the highest powers of all prime factors: 2^3 * 3^2 * 11 = 792.

3. LCM(25, 75, 120): - Prime factorization of 25: 5^2 - Prime factorization of 75: 3 * 5^2 - Prime factorization of 120: 2^3 * 3 * 5 - The LCM is the product of the highest powers of all prime factors: 2^3 * 3 * 5^2 = 600.

4. LCM(17, 34, 51): - Prime factorization of 17: 17 - Prime factorization of 34: 2 * 17 - Prime factorization of 51: 3 * 17 - The LCM is the product of the highest powers of all prime factors: 2 * 3 * 17 = 102.

Summary of the Least Common Multiples (LCMs):

- LCM(34, 64) = 1088 - LCM(99, 88) = 792 - LCM(25, 75, 120) = 600 - LCM(17, 34, 51) = 102

Please let me know if there's anything else I can help you with!