LCD of 1/25 + 3/49 + 7/125 + 5/64 + 1/7 = ? It’s EASY- the Lowest Common Denominator of FRACTIONS!

How to find the LCD(lowest common denominator) of fractions. Learn more math at TCMathAcademy.....
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[@2012mssunshine]

I needed this in school. I’m learning what I wasn’t interested in now.

[@dazartingstall6680]

First off, let's add the obvious ones we can do in our head:
1/25 + 7/125 = 12/125
3/49 + 1/7 = 10/49
So we have:
12/125 + 10/49 + 5/64
For prime factors of the denominators, that gives us:
5³, 7², 2⁶
In other words, no common factors. So we just multiply the three denominators:
LCD = 125 × 49 × 64 = 392,000
Just for completion's sake:
37,623/392,000 + 80,000/392,000 + 30,625/392,000 = 148,257/392,000

[@panlomito]

Thanks... I also wanted to do the last step but got scared of the big numbers to do the math without calculator.

[@lj6079]

Yes got it right with calculator else I'd still be counting beans 😂

[@louf7178]

Good refresher. This often trips me up.

[@timwong8556]

(2^6)(7^2)(5^3) = 64*49*125 = 392,000.
(Did not show my work for prime factorization of each number )

[@russelllomando8460]

got 392,000 49 x 125 x 64 25 & 7 are already included. thanks for the fun

[@GetMeThere1]

By inspection it's easy to see that it's 49 x 125 x 64 = 392,000. 7 and 25 are covered.

[@panlomito]

25 = 5 . 5 (included in 125)
49 = 7 . 7
125 = 5 . 5 . 5
64 = 2 . 2 . 2 . 2 . 2 . 2
7 = 7 (included in 49)
So the LCD = 49 . 125 . 64 = 49 . 250 . 32 = 49 . 500 . 16 = 49 . 1000 . 8 = 49 . 8000 = 50 . 8000 - 8000 =
400000 - 8000 = 392000 and no calculator needed.

[@user-ic8mt6jq1z]

1/25 + 3/49 + 7/125 + 5/64 + 1/7 = ?
prime factorization :
25 = 5 * 5 = 5^2 , 49 = 7 * 7 = 7^2, 125 = 5 * 5 * 5 = 5^3 , 64 = 2 * 2 * 2 * 2 * 2 *2 = 2^6, 7 = 7^1
the highest power of each : 7^2 * 5^3 * 2^6 = 49 * 125 * 64 = 392000 LCD
392000 / 25 (1 ) = 15680 , 392000 / 49(3) = 24000, 392000 / 125(7) = 21952 , 392000 / 64(5) = 30625 , 392000 / 7(1) = 56000
15680/392000 + 24000/392000 + 21952/392000 + 30625/392000 + 56000/392000 = 148257/392000 = 0.379 or 148257/392000 = (1.48257 * 10^5) / (3.92 * 10^5) = 1.48257/3.92 = 0.379

[@InPursuitOfCuriosity]

I really great instruction on how to find the LCD, thanks.

[@josephlaura7387]

Thank you

[@daveb7999]

Thanks for this!🐘

[@chrisdissanayake6979]

Lowest Common Denominator (LCD) of 25, 49, 125, 64, 7
( 25 and 125 can be divided by 25. 49 and 7 can be divided by 7)
25 I 25, 49, 125, 64, 7
I----------
7 I 1, 49, 5, 64, 7
I ----------
1, 7, 5, 64, 1
That’s all we can do. So, we multiply all the numbers left:
25 x 7 x 1 x 7 x 5 x 64 x 1 = 392,000
The LCD is 392,000

[@tonyb7779]

My reasoning exactly. It took about 2 seconds of logic in my head.

[@Matlockization]

You definitely got my attention with this maths question.

[@thomasharding1838]

125 x 64 x 49 = 392000 125 takes care of the 25 and 49 the 7.

[@johnplong3644]

You factor the denominators that is a clue .

[@DanielDimov358]

But why should the highest exponent power of a certain prime factor be taken? Is there a reason for that?

[@dazartingstall6680]

Because we're looking for the *lowest* common multiple. If we're multiplying by 125 (ie, 5³) in order to make the result divisible by 125, we know that the result will automatically be a multiple of 25 (ie 5²) so there's no need to also multiply by 25. Doing so would make the result larger than needed.
An even simpler example: The LCM of 4 and 8 is 2³, ie 8. Note that finding this by prime factorisation would require us to discard the 2² which results from factorising 4.

[@DanielDimov358]

​@@dazartingstall6680 That makes clearer. I appreciate the help.

[@gopherspace8571]

Wow great lesson 👍👋🙏💪😎🌎

[@michaelaustin-xx7cu]

392,000 did it the old time way

[@richardsmith3905]

392,000

[@johnfranklin7260]

If the power was a fraction, what then?

[@Matlockization]

Then the denominator part of the fraction power turns into a square root. The typical square root has an invisible 2 in front, but a cube root would have a 3 in front of the square root sign.

[@2012mssunshine]

Math time.

[@JolysaA]

1^25 + 3^49+7^125+5^64+1-7 = 203