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 |
|---|---|
| 56 and 113 | 6328 |
| 139 and 29 | 4031 |
| 97 and 149 | 14453 |
| 196 and 154 | 2156 |
| 65 and 136 | 8840 |