What is the least common multiple of the greatest common factor of 46 and 115

What is the least common multiple of the greatest common factor of 46 and 115

The greatest common factor is 23 and the least common multiple is 230
It can be done by short division
┎46 115
23┎2 5
The greatest common factor of 46 and 115 is 23
The least common multiple is 23 * 2 * 5 = 230

The least common multiple of 32 and 6, the least common multiple of 18 and 12, the least common multiple of 8 and 3, the least common multiple of 42 and 14, and the least common multiple of 24 and 18

First of all, write out the prime factors of two numbers, and the least common multiple is equal to the product of all their prime factors (if several prime factors are the same, compare which of the two numbers has more prime factors and multiply more times)
For example, find the least common multiple of 45 and 30
45=3*3*5
30=2*3*5
The different prime factors are 2, 3 and 5.3, which are both of them. Because 45 has two 3's and 30 has only one 3's, the least common multiple is multiplied by two 3's
The least common multiple is equal to 2 * 3 * 3 * 5 = 90
Another example is to calculate the least common multiple of 36 and 270
36=2*2*3*3
270=2*3*3*3*5
The different prime factor is 5.2, which is more than two in 36, so it is multiplied twice; 3, which is more than 270, is three, so it is multiplied three times
The least common multiple is equal to 2 * 2 * 3 * 3 * 5 = 540
According to this method to do OK Oh! Very simple!

What is the greatest common factor of 48 and 32______ The least common multiple is______ ．

The greatest common factor of 32 = 2 × 2 × 2 × 2 × 248 = 2 × 2 × 2 × 2 × 332 and 48 is 2 × 2 × 2 = 16, and the least common multiple of 32 and 48 is 2 × 2 × 2 × 2 × 2 × 3 = 96

How many five digit numbers without repetition can be formed by using the five numbers 01234, i.e. even numbers larger than 21034

3****：3*3!=18
4****：2*3!=12
23***：2*2!=4
24***：1*2!=2
213**：2
214**：1
18+12+4+2+2+1=39

01234 is composed of five digits. How many even numbers are there without repetition?

1. If the digit is 0, there are 12 kinds of C4 (1) * C3 (1);
2. If the individual bit is 2 or 4, there are 18 kinds of 2 * C3 (1) * C3 (1)
There are 12 + 18 = 30 species

01234 how many even 3-digit numbers are there

All the three digits of 01234 are: C (4,1) * C (4,1) * C (3,1) = 4 * 4 * 3 = 48
Note that 0 cannot be a hundred
The three odd numbers of 01234 are: C (2,1) * C (3,1) * C (3,1) = 2 * 3 * 3 = 18
therefore
01234 the even number of 3 digits without repetition is 48-18 = 30

How many different four digit numbers can be formed with the number 01234? It is not allowed to repeat. What is the sum of all four digit numbers

(1) The different four digit numbers are
4 × 4 × 3 × 2 = 96
(2) There are 1, 2, 3 and 4 in the thousand
4 × 3 × 2 = 24
There are 100, 10, 1, 2, 3 and 4 in each position
3 × 3 × 2 = 18
The sum of all four digits is
（1+2+3+4）×24×1000+（1+2+3+4）×18×（100+10+1）
=240000+24×18×111
=287952

Choose an even number and three odd numbers from the ten numbers of 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to form a four digit number without repetition. Such four digits have ()
A. 1480 B. 1440 C. 1200 D. 1140

The even number 0 is a restricted element. For 0 classification, when the even number is not 0, select an even number, 4 odd numbers, 3 odd numbers, C53 = 10, and then arrange a44 completely. According to the step-by-step counting principle, the total number of a44 is 4c53a44 = 960. When the even number is 0 and the odd number is 3, C53 = 100, the first place can only be placed in the second, third and fourth place. The remaining three positions are arranged completely by 3 odd numbers. The total number of a44 is c53a31a333 = 180, and the total number of a44 is 9 60 + 180 = 1140, so D

How many even four digit numbers ()
A. 6B. 10C. 12D. 24

When the last digit is 0, the first three digits are randomly arranged with A33 = 6. When the last digit is 2, the first digit can only be selected from 1 and 3, and then the middle two digits are arranged with A12 · A22 = 4. According to the principle of classification and counting, there are 6 + 4 = 10 even digits without repetition

How many even 4-digit numbers without repetition can be made up of six numbers 0.1.2.3.4.5

Classification:
(1) The last digit is 0, the other three digits are unlimited, and a (5,3) = 5 * 4 * 3 = 60
(2) The last position is 2 or 4, the highest position cannot be 0, there are four choices, the other two are unlimited, there are a (4,2) possibilities
2*4*A(4,2)=96
Therefore, there are 60 + 96 = 156 even 4-digit numbers without repetition