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
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
| Divisor | 6 | 8 | 9 | 12 |
| 2 | 3 | 4 | 9 | 6 |
| 3 | 1 | 4 | 3 | 2 |
| 2 | 1 | 2 | 3 | 1 |
| 2 | 1 | 1 | 3 | 1 |
| 3 | 1 | 1 | 1 | 1 |
- Find the factors of the first number, 6 = 2 x 3.
- 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
- 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
- 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,
- 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 6 | Multiples of 8 | Multiples of 9 | Multiples of 12 |
| 6 | 8 | 9 | 12 |
| 12 | 16 | 18 | 24 |
| 18 | 24 | 27 | 36 |
| 24 | 32 | 36 | 48 |
| 30 | 40 | 45 | 60 |
| 36 | 48 | 54 | 72 |
| 42 | 56 | 63 | 84 |
| 48 | 64 | 72 | 96 |
| 54 | 72 | 81 | 108 |
| 60 | 80 | 90 | 120 |
| 72 | 88 | 99 | 132 |
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)
[contact-form-7 404 "Not Found"]You can find more examples here
[…] Prev: Prime FactorizationNext: LCM […]