How can you the least find denominator for 1/8 and 2/9?

Question

Luna Angel · Accepted Answer

#72#

First, find the prime factorization of each denominator:

#8 = 2xx2xx2 = 2^3# #9 = 3xx3 = 3^2#

Next, find the product of the greatest powers of each prime that occurs:

#2^3xx3^2 = 8xx9 = 72#

In this case, the least common denominator is #72#.

#1/8 = (1xx9)/(8xx9) = 9/72# #2/9 = (2xx8)/(9xx8) = 16/72#

In the above case, we get the same result by just multiplying the two denominators. For an example where that is not the case, consider #1/12# and #1/18#

#12 = 2xx2xx3 = 2^2xx3^1# #18 = 2xx3xx3 = 2^1xx3^2#

The only primes which appear are #2# and #3#. The greatest power of #2# is #2^2#. The greatest power of #3# is #3^2#. Multiplying them, we get

#2^2 xx 3^2 = 4xx9 = 36#

So the least common denominator between #1/12# and #1/18# is #36#.

#1/12 = (1xx3)/(12xx3) = 3/36# #1/18 = (1xx2)/(18xx2) = 2/36#

Levi Adams · Answer

undefined To find the least common denominator for 1/8 and 2/9, first, determine the prime factors of the denominators:

For 1/8, the denominator 8 factors into 2^3.
For 2/9, the denominator 9 factors into 3^2.

The least common denominator (LCD) must include all the unique prime factors with their highest exponent from both denominators. In this case, the LCD would be 2^3 * 3^2 = 72.

Therefore, the least common denominator for 1/8 and 2/9 is 72.