Least Common Multiple (LCM) of 34 and 127
The least common multiple (LCM) of 34 and 127 is 4318.
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 127?
First, calculate the GCD of 34 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 127 = 0 remainder 34 |
| 2 | 127 ÷ 34 = 3 remainder 25 |
| 3 | 34 ÷ 25 = 1 remainder 9 |
| 4 | 25 ÷ 9 = 2 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 169 | 17745 |
| 150 and 108 | 2700 |
| 167 and 38 | 6346 |
| 66 and 57 | 1254 |
| 38 and 68 | 1292 |