Question

Find the lowest common denominator for the fractions shown? 8/51 19/85

Answer 1

the easiest way is to find the prime factors of each number

to do this, you should learn (memorize) the first few (as many as you can manage!) prime numbers:
2 3 5 7 11 13 17 19 23 29
Here is a longer
list http://www.mathsisfun.com/numbers/prime-numbers-to-10k.html

2nd, you should learn some rules for what numbers will evenly divide into another number. Try to learn these rules
http://www.mathsisfun.com/divisibility-rules.html

using the rule that if the sum of the digits is divisible by 3 then the number is divisible by 3 we figure out that 51 (digits 5+1=6 and 6/3 works) is divisible by 3. we get
3,17 From our list of prime numbers we know we have all the prime factors because 17 is prime

now find the prime factors of 85
from the rule that if a number ends in 0 or 5 it is divisible by 5. we divide 5 into 85 to get 17
5*17 are the prime factors of 85


we have
3*17 and 5*17
to find the least common denominator we take a combination
3*5*17 ( notice that 3*17 divides into this number and so does 5*17)
that is our common denominator

now do your problem
83⋅17+195⋅17

you need to multiply the bottom of the 1st fraction by 5 to get the common denominator. And mult the bottom of the 2nd fraction by 3:
83⋅17⋅55+195⋅17⋅33

you get
8⋅53⋅5⋅17+19⋅33⋅5⋅17

8⋅5+19⋅33⋅5⋅17

multiply 5*8 to get 40 and 3*19 to get 57
40+573⋅5⋅17

add to get
973⋅5⋅17

we should multiply out the denominator to get
97255

Answer 2

First, find the prime factors of 51 and 85.
The prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, ...
To find the prime factors of a number, try to divide the number by each one of the prime numbers starting with 2. Divide it by each prime as many times as possible. Then move on to the next prime number, and keepo on going until you get 1.

Let's try 51. It's not divisibble by 2, so let's try 3:
51/3 = 17. 17 is a prime number, so
17/17 = 1
This means that 51 = 3 * 17

Now let's do 85:
85 is not divisible by 2 or 3, but it is divisible by 5.
85/5 = 17
17/17 = 1
85 = 5 * 17

Now we have
51 = 3 * 17
85 = 5 * 17

To get the LCD, or LCM, of two numbers, you need every factor that is in either number, and if the same factor shows in both numbers, choose the one with the huigher exponent. In this case, you need 3, 5, and 17.
Multiply those prime factors together and you get your LCD.
LCD = 3 * 5 * 17 = 255