Least Common Multiple (LCM) of 106 and 108
The least common multiple (LCM) of 106 and 108 is 5724.
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 108?
First, calculate the GCD of 106 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 108 = 0 remainder 106 |
| 2 | 108 ÷ 106 = 1 remainder 2 |
| 3 | 106 ÷ 2 = 53 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 168 | 840 |
| 106 and 152 | 8056 |
| 134 and 108 | 7236 |
| 191 and 53 | 10123 |
| 130 and 96 | 6240 |