Least Common Multiple (LCM) of 114 and 117
The least common multiple (LCM) of 114 and 117 is 4446.
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 114 and 117?
First, calculate the GCD of 114 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 117 = 0 remainder 114 |
| 2 | 117 ÷ 114 = 1 remainder 3 |
| 3 | 114 ÷ 3 = 38 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 110 | 3410 |
| 83 and 66 | 5478 |
| 78 and 29 | 2262 |
| 200 and 103 | 20600 |
| 171 and 56 | 9576 |