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 |
|---|---|
| 170 and 176 | 14960 |
| 156 and 134 | 10452 |
| 172 and 52 | 2236 |
| 131 and 165 | 21615 |
| 146 and 133 | 19418 |