Least Common Multiple (LCM) of 117 and 83
The least common multiple (LCM) of 117 and 83 is 9711.
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 83?
First, calculate the GCD of 117 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 83 = 1 remainder 34 |
| 2 | 83 ÷ 34 = 2 remainder 15 |
| 3 | 34 ÷ 15 = 2 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 71 | 3621 |
| 142 and 50 | 3550 |
| 177 and 199 | 35223 |
| 184 and 70 | 6440 |
| 65 and 200 | 2600 |