Least Common Multiple (LCM) of 108 and 117
The least common multiple (LCM) of 108 and 117 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 108 and 117?
First, calculate the GCD of 108 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 117 = 0 remainder 108 |
| 2 | 117 ÷ 108 = 1 remainder 9 |
| 3 | 108 ÷ 9 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 117 | 14274 |
| 57 and 87 | 1653 |
| 126 and 86 | 5418 |
| 161 and 104 | 16744 |
| 112 and 168 | 336 |