Least Common Multiple (LCM) of 13 and 106
The least common multiple (LCM) of 13 and 106 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 13 and 106?
First, calculate the GCD of 13 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 106 = 0 remainder 13 |
| 2 | 106 ÷ 13 = 8 remainder 2 |
| 3 | 13 ÷ 2 = 6 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 19 | 3306 |
| 166 and 16 | 1328 |
| 148 and 83 | 12284 |
| 105 and 133 | 1995 |
| 130 and 71 | 9230 |