Least Common Multiple (LCM) of 106 and 13
The least common multiple (LCM) of 106 and 13 is 1378.
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 13?
First, calculate the GCD of 106 and 13 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 13 = 8 remainder 2 |
| 2 | 13 ÷ 2 = 6 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 193 | 25862 |
| 188 and 162 | 15228 |
| 193 and 110 | 21230 |
| 128 and 137 | 17536 |
| 80 and 198 | 7920 |