what are the lcm of 6ab^2 and 18ab^3

Question

i need help with finding the LCM for 6ab^2 and 18ab^3 also 12a^2 please and thank you

Answer 1

Hello Bethany,

To find LCM first list prime factors of all the terms. The terms can be written as

6ab² = 2.3.a.b²

18ab³ = 2.3².a.b³

12a² = 2².3.a²

After this multiply each factor the greatest number of times it occurs in either number. if the same factor occurs more than once in both terms, you multiply the factor the greatest number of times it occur.

2: two occurrences

3: two occurrences

a: two occurrences

b: three ocurrences

2².3².a².b³= 36a²b³ (LCM) ---------answer

I hope this helps.

 

Answer 2

Remember there is LCM and GCF and the weird thing about them is that the one that starts with the letter L ends up being greater and the one that starts with G ends up being less.

Let's identify these guys as first, second and third term -->

1T: 6ab^2  

2T: 18ab^3

3T: 12a^2

So one easy way to do it would be to start with the coefficients, which are 6, 18 and 12 and list their multiples:

6, 12, 18, 24, 30, 36...

18, 36, 48...

12, 24, 36, 48...

Now for the confusing stuff, the a's and b's: 

Just take the highest number any term has for either.  You can think of listing them out again, but I can only explain so much in these little boxes.  2T has 3b's and 3T has 2 a's, so your LCM ends up being:

36a^2b^3