Least Common Multiple (LCM) of 107 and 117
The least common multiple (LCM) of 107 and 117 is 12519.
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 107 and 117?
First, calculate the GCD of 107 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 117 = 0 remainder 107 |
| 2 | 117 ÷ 107 = 1 remainder 10 |
| 3 | 107 ÷ 10 = 10 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 195 | 33735 |
| 125 and 172 | 21500 |
| 177 and 53 | 9381 |
| 140 and 141 | 19740 |
| 106 and 83 | 8798 |