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 |
|---|---|
| 128 and 106 | 6784 |
| 120 and 64 | 960 |
| 142 and 45 | 6390 |
| 80 and 105 | 1680 |
| 63 and 68 | 4284 |