Least Common Multiple (LCM) of 34 and 122
The least common multiple (LCM) of 34 and 122 is 2074.
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 34 and 122?
First, calculate the GCD of 34 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 122 = 0 remainder 34 |
| 2 | 122 ÷ 34 = 3 remainder 20 |
| 3 | 34 ÷ 20 = 1 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 141 | 20868 |
| 105 and 84 | 420 |
| 163 and 130 | 21190 |
| 144 and 45 | 720 |
| 141 and 124 | 17484 |