Least Common Multiple (LCM) of 117 and 86
The least common multiple (LCM) of 117 and 86 is 10062.
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 86?
First, calculate the GCD of 117 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 86 = 1 remainder 31 |
| 2 | 86 ÷ 31 = 2 remainder 24 |
| 3 | 31 ÷ 24 = 1 remainder 7 |
| 4 | 24 ÷ 7 = 3 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 139 | 18626 |
| 135 and 117 | 1755 |
| 56 and 191 | 10696 |
| 84 and 88 | 1848 |
| 188 and 99 | 18612 |