3 Easy Steps to Enjoy Lowest Common Denominator

The lowest common denominator is the smallest number which all the numbers can be divided into. The lowest common denominator is also called as least common multiple(lcm).

It is termed as common factors x uncommon factors

Lowest common denominator - student learning lcm
Lowest common denominator

How do you find the lowest common denominator?

The following are three methods to find the lowest denominator.

1. Lowest Common Denominator – Division Method

In this method divide, all the numbers till the remainder are 1. For example lcm of 6,8,9 and 12

Divisor68912
23496
31432
21231
21131
31111
Lowest common denomination – division method
  1. Find the factors of the first number, 6 = 2 x 3.
  2. Take the first factor and divide it by each. 6,8 and 12 when divided by 2 give 3,4 and 6 respectively. As 9 is not divisible by 2. Keeping 9 as it is
  3. Taking the other prime number 3 and dividing the numbers 3 and 6 which gives the division as 1 and 2. Repeat the process until every factor’s remainder is 1
  4. Multiply the divisors 2 x 3 x 2 x 2 x 3 = 72

So the lcm or least common denomination is 72

2. Least Common Multiple – Prime Factorization Method

In the prime factorization method, we find the prime factors of the numbers. Considering the same example,

  1. factors are:

6 = 2 x 3

8 = 2 x 2 x 2

9 = 3 x 3

12 = 2 x 2 x3

2. Find common factor between all numbers, in this case it is 1

3. Find common factors between maximum numbers.

The common factor between 6, 8, and 12 is 2

The common factor between 6, 9, and 12 is 3

4. Find the remaining uncommon factors from all the numbers:

uncommon factors in 6 are 1, in 8 is 2 x 2, 9 is 3, 12 is 1

5. Common factors x uncommon factors = 2 x 3 x 2 x 2 x 3 = 72

3. Listing the Multiples

Multiples of 6Multiples of 8Multiples of 9Multiples of 12
68912
12161824
18242736
24323648
30404560
36485472
42566384
48647296
547281108
608090120
728899132
Lowest Common Denominator – Multiples Method

After listing the multiples the smallest common number between all the numbers is 72

therefore lcm of 6, 8, 9, and 12 is 72

Questions below are taken from a book of an author R.S.Agarwal.

FAQ: Detailed answer can be found in pdf below

12

17

79

360

198

2/3

3/5

20/54 = 10/27

0.9

2.7

2^2 x 3^5 x 7^2

12,24, 36

27, 27×7

Total 4 pairs

Total 4 pairs

12×4, 12×3

111

Total pairs are 3

Download a Free pdf Sample of Examples(Questions from the book R.S. Agarwal)

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You can find more examples here

least common multiplication

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