Least Common Multiple (LCM) of 107 and 34
The least common multiple (LCM) of 107 and 34 is 3638.
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 107 and 34?
First, calculate the GCD of 107 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 34 = 3 remainder 5 |
| 2 | 34 ÷ 5 = 6 remainder 4 |
| 3 | 5 ÷ 4 = 1 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 20 | 180 |
| 177 and 55 | 9735 |
| 30 and 93 | 930 |
| 21 and 59 | 1239 |
| 36 and 122 | 2196 |