Least Common Multiple (LCM) of 106 and 134
The least common multiple (LCM) of 106 and 134 is 7102.
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 134?
First, calculate the GCD of 106 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 134 = 0 remainder 106 |
| 2 | 134 ÷ 106 = 1 remainder 28 |
| 3 | 106 ÷ 28 = 3 remainder 22 |
| 4 | 28 ÷ 22 = 1 remainder 6 |
| 5 | 22 ÷ 6 = 3 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 121 | 3872 |
| 13 and 129 | 1677 |
| 128 and 106 | 6784 |
| 59 and 121 | 7139 |
| 193 and 197 | 38021 |