What is the least common multiple of 6,9, and 10?

4 Answers
Nov 7, 2017

1

Explanation:

The only number 6, 10, and 9 can be divided by without a decimal is 1. This can be displayed by trying all the factors of one number, and trying them with the others. Let's try using 6.

Here are all of 6's factors:
6 -: 6 = 1
6 -: 3 = 2
6 -:2 = 3
6 -:1 = 6

1, 2, 3 or 6.

Now try to divide another number by each of these. Let's try 10.

10 -: 1 = 10 sqrt
10 -: 2 = 5 sqrt
10 -: 3 = 3.333... xx
10 -: 6 = 1.666... xx

Both 1 and 2 worked. Now, we try this with 9.

9 -: 1 = 9 sqrt
9 -: 2 = 4.5 xx

The only number left is 1, so this is your LCM.

Nov 8, 2017

90

Explanation:

one approach is to list the multiples and pick out the common ones

multiples of

6:{6,12,18,24,30,36,42,48,54,60,66,72,78,84,color(red)(90),96,..}

multiples of

9:{9,18,27,36,45,54,63,72,81,color(red)(90),99,...}

multiples of

10:{10,20,30,40,50,60,70,80,color(red)(90),100,..}

from the lists one can see that the

least common multiple is 90

Nov 8, 2017

LCM = 90

Explanation:

Note that of the numbers given, 9 and 10 are consecutive numbers.

The LCM of two consecutive numbers is always their product.

So without other working we can immediately consider

9xx10=90" " as the LCM.

But will this work for 6 as well?

6 =2xx3

3 is a factor of 9 and 2 is a factor of 10, so 90 is also a multiple of 6

Nov 8, 2017

The LCM of 6, 9, and 10 is color(purple)90.

Explanation:

Another method for determining the least common multiple (LCM) is using prime factorization. List the prime factors for each number. Then multiply each prime factor the greatest number of times it appears in any one factorization.

Find the LCM of 6, 9, and 10 by listing the prime factors of each number.

6:color(red)2xx3

9:color(blue)3xxcolor(blue)3

10:2xxcolor(green)5

Multiply each prime factor the greatest number of times it appears in any one factorization.

LCM: color(red)2xxcolor(blue)3xxcolor(blue)3xxcolor(green)5=90