Question

Знайди найменше спільне кратне чисел. а) НСК (62; 496); б) НСК (31; 186). Пожалуйста! Очень срочно! ​

Answer 1

Ответ:

496 ; 186

Пошаговое объяснение:

НСК ( 62 ; 496 )

Спочатку розкладено числа на прості множники :

62 = 2 * 31

496 = 2 * 2 * 2 * 2 * 31

НСК ( 62; 496 ) =  2 * 2 * 2 * 2 * 31 = 2⁴* 31 =496

НСК ( 31;186)

31 - просте число

186 = 2 * 3 * 31

НСК ( 31 ; 186) = 2* 3* 31 = 186

Answer 2

Finding the least common multiple (LCM) of two numbers

To find the least common multiple (LCM) of two numbers, we need to determine the smallest number that is divisible by both numbers. There are several methods to find the LCM, including prime factorization, listing multiples, and using the LCM formula.

Let's find the LCM of the given numbers:

a) LCM(62, 496) b) LCM(31, 186)

Method 1: Prime Factorization

One way to find the LCM is by using prime factorization. We can express each number as a product of its prime factors and then take the highest power of each prime factor that appears in either number.

a) LCM(62, 496): - Prime factorization of 62: 2 * 31 - Prime factorization of 496: 2^4 * 31

To find the LCM, we take the highest power of each prime factor: 2^4 * 31 = 496.

b) LCM(31, 186): - Prime factorization of 31: 31 - Prime factorization of 186: 2 * 3 * 31

To find the LCM, we take the highest power of each prime factor: 2 * 3 * 31 = 186.

Therefore, the LCM of (62, 496) is 496 and the LCM of (31, 186) is 186.

Method 2: Listing Multiples

Another method to find the LCM is by listing multiples of each number until we find a common multiple.

a) LCM(62, 496): - Multiples of 62: 62, 124, 186, 248, 310, 372, 434, 496 - Multiples of 496: 496, 992, 1488, 1984, 2480, 2976, 3472, 3968

The first common multiple is 496, so the LCM of (62, 496) is 496.

b) LCM(31, 186): - Multiples of 31: 31, 62, 93, 124, 155, 186 - Multiples of 186: 186, 372, 558, 744, 930, 1116, 1302, 1488

The first common multiple is 186, so the LCM of (31, 186) is 186.

Method 3: LCM Formula

The LCM can also be found using the LCM formula, which states that LCM(a, b) = (a * b) / GCD(a, b), where GCD is the greatest common divisor.

a) LCM(62, 496): - GCD(62, 496) = 2 - LCM(62, 496) = (62 * 496) / 2 = 496

b) LCM(31, 186): - GCD(31, 186) = 31 - LCM(31, 186) = (31 * 186) / 31 = 186

Using the LCM formula, we find that the LCM of (62, 496) is 496 and the LCM of (31, 186) is 186.

In conclusion, the least common multiple (LCM) of the given numbers is as follows: a) LCM(62, 496) = 496 b) LCM(31, 186) = 186.

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