Least Common Multiple (LCM) of 115 and 106
The least common multiple (LCM) of 115 and 106 is 12190.
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 115 and 106?
First, calculate the GCD of 115 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 106 = 1 remainder 9 |
| 2 | 106 ÷ 9 = 11 remainder 7 |
| 3 | 9 ÷ 7 = 1 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 55 | 10945 |
| 160 and 82 | 6560 |
| 28 and 97 | 2716 |
| 79 and 122 | 9638 |
| 119 and 114 | 13566 |