Least Common Multiple (LCM) of 108 and 113
The least common multiple (LCM) of 108 and 113 is 12204.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 108 and 113?
First, calculate the GCD of 108 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 113 = 0 remainder 108 |
| 2 | 113 ÷ 108 = 1 remainder 5 |
| 3 | 108 ÷ 5 = 21 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 55 | 6160 |
| 43 and 159 | 6837 |
| 189 and 84 | 756 |
| 123 and 158 | 19434 |
| 141 and 27 | 1269 |