Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 261

L.C. Denominator for several values

Lowest common denominator for;

1/3  2/9  1/4  3/16  3/10 ?

Where do you start if you don’t see it immediately?
I know I can multiply all the denominators together to get a common denominator (but not necessarily the lowest one)
3*9*4*16*10=17,280

But how do I get the lowest one?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,524

Re: L.C. Denominator for several values

1/3  2/9  1/4  3/16  3/10

Reduce each demoninator to its prime factors

3 = 3
9 = 3x3
4 = 2x2
16 = 2x2x2x2
10 = 2x5

Write the largest power of each prime and multiply them

(2x2x2x2) x (3x3) x 5

That's the only way to make sure that 16 and 9 go into it.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 261

Re: L.C. Denominator for several values

Ah, ingenious.

Thanks, Bob.

About your Galileo quote; has he borrowed/developed that from Socrates/Plato. I think Socrates, or Plato putting words in Socrates' mouth, said something similar. Socrates would try to help his interlocutor 'give birth' to insights. Socrates was sometimes known as the midwife due to this. Also, his mother might have actually been a midwife.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,524

Re: L.C. Denominator for several values

I tried googling that quote again and most hits attribute it to Galileo but a similar one  "I cannot teach anybody anything, I can only make them think" is attributed to Socrates.  I think you're right.  Galileo would have read Socrates and the two quotes are very similar especially when you take account of translation variations.

A modern version is "You can lead a horse to water, but you can't make him drink."

You can also use the method to find the highest common factor.

eg. Find the HCF of 45 and 72

45 =                 3 x 3 x 5
72 = 2 x 2 x 2 x 3 x 3

This time extract all the primes that occur in both.  So 3 x 3

If you create a Venn diagram with all the primes and each circle enclosing those for one of the  numbers then the lowest common multiple (LCM) is the union of the sets and the HCF is the intersection.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

woodturner550

Member

Registered: 2024-06-08

Posts: 24

Re: L.C. Denominator for several values

This is how I was taught. Thought process first.
1/3  2/9          1/4  3/16  3/10      original
split problem:
1/3+2/9                                                         
1/3  2/9 = 3/9 + 2/9 = 5/9

1/4  3/16  3/10 = 4/16 + 3/16 = 7/16 + 3/10
7/16 + 3/10 = 21/160
21/160+5/9 = 105/1440 are /5
21/288

woodturner550

Bob

Administrator

Registered: 2010-06-20

Posts: 10,524

Re: L.C. Denominator for several values

hi woodturner550

7/16 + 3/10 = 21/160

note. LCM of 16 and 10 is 80.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

woodturner550

Member

Registered: 2024-06-08

Posts: 24

Re: L.C. Denominator for several values

My bad! Thanks for pointing it out. I don't do fraction very often. Not an excuse.