whats the common denominator for....?

Question

common denaminator for

a)3/10, 5/6,-3/4

b)1/8,14/15,4/7

c)1/6,14/5,13/28

d)7/15,23/20,5/6

and pls tell me how to do it, i know most of time, you multiply the numbers but sometimes the product is too high. can you guys give me some ideas how to find the commion factor?

thanks in advance

Answer 1

To solve for least common denominator without multipling the numbers together, factor each.

For a:
10 = 2*5
6 = 2*3
4= 2*2

To figure the least common factor, you need to have each factor from each of the numbers:

Each has one 2, so you will need one 2.
10 has a 5, so you need a 5
6 has a 3, so you need a 3
4 has a 2nd 2, so you need a 2nd 2:

2*2*3*5 (fifteentimestwoisthirtytimestwois...)

60!

Answer 2

yes multiply the numbers together
but if they have common factors then as you say the number is larger than it need be

let's look at the 1st one
3/10, 5/6,-3/4

now 10 = 2*5 ...the 2 is present in 6 and 4
the factors that are NOT shared are
5 and 3

so we need a 5, a 3 and the 2 and another 2 (to make 4)
ie 60 is divisble by 10 and 6 and 4

===========
b)1/8,14/15,4/7

8, 14 and 7 ...lots of 2's and 7

8*7 = 56 (and the 14 must go as it only needs a 2 and a 7)


HTH

Answer 3

common denominator is found by finding the LCM of denominators
a)
LCM of 10, 6 , 4
10 = 2*5
6 = 2*3
4 = 2*2
2 is common in all, so LCM is 2* product remaining factors
(2) (5)(3)(2) = 60

b)
LCM of 8, 15, 7
8 = 2*2*2
15 = 3*5
7 = 7
there is no common factor
so LCM or coomon denominator = (8)(15)(7) = 840

c)
6, 5, 28
6 = 2*3
5 = 5
28 = 2*2*7
LCM = 2[3*5*2*7]= 420

d)
15, 20, 6

15 = 3*5
20 = 2*2*5
6 = 2*3
2 is common in 20 and 6, 3 is common in 15 and 6 and 5 is common in 15 and 20
LCM = 2*3*5[2] = 60

Answer 4

If you have two or more even numbers, you can usually reduce the product of the 3 numbers to a lower common denominator by dividing by at least 2, or if you have 3 even numbers, by checking if the product of two of the numbers is divisible by the third.

So in a, 6*10=60, which is also divisible by 4. So the answer is 60

In b, you have to take the product of 3.
In c, the same deal.
In d, 15*20 is divisible by 6, so your answer is 300.

Answer 5

I would simply just multiply by the denominator throughout the top.

a) (3/10)* (6*4) = -72/240
(5/6) *(10*-4)= -200/240
(-3/4) *(10*5)= -150/240

From there you can reduce

so 36/120 100/120 -75/120

Apply that process to the rest.

Answer 6

a) 60 b)840 c)420 d)60

Obtain factors and its exponent of every number.
Take the bigger exponent of every factor.
Select all factors with your bigger exponent.
Multiply all.