How to calculate the least common multiple and the greatest common divisor

How to calculate the least common multiple and the greatest common divisor

Firstly, the definition is given, the greatest common divisor refers to the greatest one of the common divisors of several natural numbers, and the least common multiple refers to the smallest one of the common multiples of several natural numbers which is greater than zero
For example: the least common multiple of 5, 9 and 12 is 180
5 = 5,9 = 3 * 3,12 = 3 * 4,9 and 12 have a common divisor 3, which only appears once in the form of multiplication, that is, 5 * 3 * 3 * 4 = 180, so the least common multiple is 180
For example, the common divisor of 12 and 30 are: 1, 2, 3, 6, where 6 is the greatest common divisor of 12 and 30
On the module of complex number
Z1, Z2 are plural numbers, proving: | z1-z2 | + | Z1 + Z2|
|z1-z2|+|z1+z2|
What number is the greatest common divisor 1 and the least common multiple 105?
105=3*5*7
So there are four combinations
3、35
5、21
7、15
3、5、7
15 and 7
3 and 35
12 and 5
If z = (1 + 3I) / (1-I), then Z=
Z = (1 + 3I) / (1-I), then z = | 1 + 3I | / | 1-I | = √ 10 / √ 2 = √ 5
The greatest common divisor of two positive integers is 7 and the least common multiple is 105
∵ 105 △ 7 = 15; 15 = 3 × 5; ∵ one of these two numbers contains a prime factor 3, the other contains a prime factor 5, ∵ the greatest common divisor of two positive integers is 7, ∵ 7 × 3 = 21; 7 × 5 = 35. Answer: these two numbers are 21 and 35
If the complex Z (1-I) = a + 3I (I is an imaginary unit, a is a real number), and z =. Z (. Z is a conjugate complex of Z), then a=______ .
Because z =. Z (. Z is the conjugate complex number of Z), so Z is a real number, Z (1-I) = a + 3I, so z = a; - z = 3, so a = - 3, so the answer is: - 3
The greatest common divisor of two positive integers is 7 and the least common multiple is 105
∵ 105 △ 7 = 15; 15 = 3 × 5; ∵ one of these two numbers contains a prime factor 3, the other contains a prime factor 5, ∵ the greatest common divisor of two positive integers is 7, ∵ 7 × 3 = 21; 7 × 5 = 35. Answer: these two numbers are 21 and 35
Given that the complex Z satisfies (1 + √ 3I) z = 1 + I, then | Z | is equal to?
z(1+√3i)=1+i
So z = (1 + I) / (1 + √ 3I)
=(1+i)(1-√3i)/[(1+√3i)(1-√3i)]
=[(1+√3)+(1-√3)i]/4
|z|=√[(1+√3)²+(1-√3)²]/4
=2√2/4
=√2/2.
Find the greatest common divisor and the least common multiple of the following groups of numbers. 1, 44 36 2, 12 72 3, 13 9
Find the greatest common divisor and the least common multiple of the group number.
1. 44 and 36
2. 12 and 72
3. 13 and 9
Find the greatest common divisor and the least common multiple of the group number
1. 44 and 36 4 396
2. 12 and 72 12 72
3. 13 and 9 1 117
The imaginary part of complex 2 + 5I conjugate complex is
The conjugate complex number is 2-5i
The imaginary part is - 5
Z = a + bi, a is the real part, B is the imaginary part