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 |
|---|---|
| 148 and 45 | 6660 |
| 155 and 162 | 25110 |
| 80 and 39 | 3120 |
| 39 and 137 | 5343 |
| 108 and 85 | 9180 |