Least Common Multiple (LCM) of 107 and 115
The least common multiple (LCM) of 107 and 115 is 12305.
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 115?
First, calculate the GCD of 107 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 115 = 0 remainder 107 |
| 2 | 115 ÷ 107 = 1 remainder 8 |
| 3 | 107 ÷ 8 = 13 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 132 | 132 |
| 82 and 110 | 4510 |
| 94 and 149 | 14006 |
| 142 and 53 | 7526 |
| 156 and 11 | 1716 |