Least Common Multiple (LCM) of 68 and 106
The least common multiple (LCM) of 68 and 106 is 3604.
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 68 and 106?
First, calculate the GCD of 68 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 106 = 0 remainder 68 |
| 2 | 106 ÷ 68 = 1 remainder 38 |
| 3 | 68 ÷ 38 = 1 remainder 30 |
| 4 | 38 ÷ 30 = 1 remainder 8 |
| 5 | 30 ÷ 8 = 3 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 57 | 9804 |
| 37 and 187 | 6919 |
| 18 and 198 | 198 |
| 180 and 165 | 1980 |
| 136 and 148 | 5032 |