Least Common Multiple (LCM) of 113 and 108
The least common multiple (LCM) of 113 and 108 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 113 and 108?
First, calculate the GCD of 113 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 108 = 1 remainder 5 |
| 2 | 108 ÷ 5 = 21 remainder 3 |
| 3 | 5 ÷ 3 = 1 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 111 | 4551 |
| 91 and 125 | 11375 |
| 181 and 200 | 36200 |
| 148 and 47 | 6956 |
| 183 and 198 | 12078 |