Factoring and Multiples

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280, 997, 1994, 3988, 4985, 6979, 7976, 9970, 13958, 19940, 27916, 34895, 39880, 55832, 69790, 139580, 279160

4

First factorise the two numbers. It is best to write the factors out in incrasing order. Whether or not you use power or exponent notation is up to you.

12 = 2.2.3 = 22*3 and 16 = 2*2*2*2 = 24. Then for the LCM, take each factor in turn. Find the maximum number of times that it appears in the factorisation of the two numbers (equivalently, find the highest power for that factor in the factorisations). Write that down for the LCM. Move to the next prime factor. Continue until you have exhausted all he factors.

So here, 2 has an exponent 2 in 12 and an exponent 4 in 16. So for the LCM, 2 must have an exponent of 4. 3 has an exponent of 1 in 12 and 0 in 16 (REMEMBER: 30 = 1). And that is the end of the factors.

So LCM = 24*31 = 48

5/6

They are 1 and 2

17 x 19 x 19

2 x 2 x 23

Sorry, but 245 is NOT the LCM of 5, 7 and 11! The Least Common Multiple (LCM) of (5,7,11) is 385.

4


mitbrij

32=2x2x2x2x2
2 to the 5th power

You need to provide two or more positive integer numbers to properly answer this question. The LCM (least common multiple) is the smallest positive whole number exactly divisible by two or more given whole numbers.

The first question you need to investigate: Is there ANYnumber that is a common factor of 21, 30, and 44 ?
If we can't find at least two of them, then we don't have to worry about "greatest".

The factors of 21 are: 1, 3, 7, and 21.
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
The factors of 44 are: 1, 2, 4, 11, 22, and 44.

The only factor common to 21, 30, and 44 is '1'.

Technically, I guess the answer to the question is 'Yes'. There is one common factor, so it's
also the greatest.

The GCF is 5.

The greatest common factor of 192 and 2,187 is 3

The LCM is: 99

23 is prime. Prime numbers don't have proper factors.

2

64

Multiply the given number by successive counting numbers.

The factors of 6 are 1, 2, 3 and 6.

The factors of 9 are 1, 3, and 9.

The factors they have in common are 1 and 3.

A single number cannot have a least common multiple because "common" refers to multiples that two or more numbers have in common. You have only one number.

4

2 x 2 x 2 x 3 x 5 x 7

4 x 210

8 x 105

7 x 120