least common multiple and greatest common factor?

Question

find the least common multiple and the greatest common factor of 48a²b³ and 72a³b²

I'm not sure what to do. Can anyone help me?

Answer 1

LCM

48a^2b^2. 72aDivide 48 and 72 and by the lowest factor possible, so that when you multiply them, you get 48 and 72 again.

So 48 and 72 are factorized side by side
|
2 |_48, 72_______
2 |_24, 36_______
2 |_12, 18_______
2 |_06, 09_______
2 |_03, 09
3 |_01, 03_______
3 |_01, 01_______

Now take all the factors, and multiply them together...
==> 2*2*2*2*3*3 = 144. That is your least common multiple. Try the same with the a's and b's, I think you'll get a^3 b^3.

HCF is similar. But factorize them seperately.
48 = 2*2*2*2*3*a*a*b*b*b
72= 2*2*2*3*3*a*a*a*b*b

Take ONLY the common digits (only the ones that are present in both, write it down below, ONCE)

HCF=2*2*2*3*a*a*b*b = 24a^2b^2. This is your highest common factor.
Anymore help, mail me.
GoodLuck!

Answer 2

The least common multiple is the smallest term,
such that both your terms will divide into it exactly.

What you do first is find all the factors of both.

48a^2b^3 = 2 * 2 * 2 * 2 * 3 * a * a * b * b * b
72a^3b^2 = 2 * 2 * 2 * 3 * 3 * a * a * a * b * b

Next, you say to yourself, what would I have to do
to the factors of 48 and 72 to make them equal?

Notice that they'll have the same factors if you
multiply 48 by 3 and if you multiply 72 by 2.

This then, is the LCM of both numbers.
It is 2 * 2 * 2 * 2 * 3 * 3 = 48 * 3 = 72 * 2 = 144.

Now do the same with the variables,
that is, make them equal.
You have to multiply one of them by 'a'
and the other one by 'b', which gives :
a * a * a * b * b * b = a^3b^3 (= LCM of variables)

So the final LCM is 144a^3b^3.

For the greatest common factor,
again use the factored forms.

48a^2b^3 = 2 * 2 * 2 * 2 * 3 * a * a * b * b * b
72a^3b^2 = 2 * 2 * 2 * 3 * 3 * a * a * a * b * b

The greatest common factor is the most
number of factors that are found in both forms.

This is three 2's, one 3, two a's and two b's.
That is, 2 * 2 * 2 * 3 * a * a * b * b
Therefore, the GCF = 24a^2b^2.

Answer 3

You have 48a²b³ and 72a³b²
48a²b³ = 2*2*2*2*3*a*a*b*b*b and 72a³b²= 2*2*2*3*3*a*a*a*b*b

The greatest common factor, or GCF, is the greatest factor that divides two numbers.

For given two numbers we have 2*2*2,3,a*a and b*b in common.
, thus GCF is 2*2*2*3*a*a*b*b = 24a²b²

The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both, so
LCM of 72 and 48 is 144, since 72*2=144 and 48*3=144.

Also, LCm of a²b³ and a³b² is a³b³, since a²b³*a is a³b³ and a³b²*b is a³b³.

So, the LCM of is 48a²b³ and 72a³b² is 144a³b³


I hope I answered your question.

Answer 4

least common multiple is 144 a(cubed) b(cubed)
greatest common factor is 24 a(squared) b(squared)

I can't write a small 2 so I've written a(squared) which means a with a small 2 above it!
Same for the 3, b(cubed) means b with a small 3.

Answer 5

72 and 1

Answer 6

LCM = 144 a3b3
GCD = 24 a2b2

LCM is divisible by both the numbers.
Both the numbers are divisible by the GCD.

Answer 7

least common multiple is 288.

GCF is 12

Answer 8

48a^2b^3 = 2^4 * 3 *a^2 * b^3
72a^3b^2 = 2^3 * 3^2 * a^3 * b^2

LCM = 2^3 * 3 * a^2 * b^2 = 24a^2b^2
GCF = 2^4 * 3^2 * a^3 * b^3 = 144a^3b^3

Answer 9

if this is a homework question that's cheating