Least Common Multiple (LCM) of 69 and 122
The least common multiple (LCM) of 69 and 122 is 8418.
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 69 and 122?
First, calculate the GCD of 69 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 122 = 0 remainder 69 |
| 2 | 122 ÷ 69 = 1 remainder 53 |
| 3 | 69 ÷ 53 = 1 remainder 16 |
| 4 | 53 ÷ 16 = 3 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 13 | 1794 |
| 69 and 189 | 4347 |
| 18 and 31 | 558 |
| 118 and 37 | 4366 |
| 68 and 65 | 4420 |