Least Common Multiple (LCM) of 106 and 115
The least common multiple (LCM) of 106 and 115 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 106 and 115?
First, calculate the GCD of 106 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 115 = 0 remainder 106 |
| 2 | 115 ÷ 106 = 1 remainder 9 |
| 3 | 106 ÷ 9 = 11 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 100 | 12900 |
| 48 and 124 | 1488 |
| 135 and 111 | 4995 |
| 41 and 78 | 3198 |
| 159 and 16 | 2544 |