Least Common Multiple (LCM) of 117 and 108
The least common multiple (LCM) of 117 and 108 is 1404.
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 117 and 108?
First, calculate the GCD of 117 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 108 = 1 remainder 9 |
| 2 | 108 ÷ 9 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 75 | 5325 |
| 177 and 144 | 8496 |
| 61 and 57 | 3477 |
| 194 and 189 | 36666 |
| 197 and 16 | 3152 |