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 |
|---|---|
| 120 and 26 | 1560 |
| 85 and 166 | 14110 |
| 55 and 192 | 10560 |
| 54 and 28 | 756 |
| 119 and 146 | 17374 |