Least Common Multiple (LCM) of 34 and 121
The least common multiple (LCM) of 34 and 121 is 4114.
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 121?
First, calculate the GCD of 34 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 121 = 0 remainder 34 |
| 2 | 121 ÷ 34 = 3 remainder 19 |
| 3 | 34 ÷ 19 = 1 remainder 15 |
| 4 | 19 ÷ 15 = 1 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 46 | 5382 |
| 28 and 190 | 2660 |
| 63 and 76 | 4788 |
| 200 and 105 | 4200 |
| 56 and 85 | 4760 |