Least Common Multiple (LCM) of 68 and 122
The least common multiple (LCM) of 68 and 122 is 4148.
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 122?
First, calculate the GCD of 68 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 122 = 0 remainder 68 |
| 2 | 122 ÷ 68 = 1 remainder 54 |
| 3 | 68 ÷ 54 = 1 remainder 14 |
| 4 | 54 ÷ 14 = 3 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 191 | 11651 |
| 185 and 71 | 13135 |
| 63 and 143 | 9009 |
| 189 and 196 | 5292 |
| 180 and 197 | 35460 |