Least Common Multiple (LCM) of 117 and 118
The least common multiple (LCM) of 117 and 118 is 13806.
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 118?
First, calculate the GCD of 117 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 118 = 0 remainder 117 |
| 2 | 118 ÷ 117 = 1 remainder 1 |
| 3 | 117 ÷ 1 = 117 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 172 | 172 |
| 16 and 78 | 624 |
| 118 and 102 | 6018 |
| 32 and 178 | 2848 |
| 112 and 73 | 8176 |