Least Common Multiple (LCM) of 107 and 39
The least common multiple (LCM) of 107 and 39 is 4173.
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 39?
First, calculate the GCD of 107 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 39 = 2 remainder 29 |
| 2 | 39 ÷ 29 = 1 remainder 10 |
| 3 | 29 ÷ 10 = 2 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 108 | 756 |
| 138 and 30 | 690 |
| 73 and 109 | 7957 |
| 188 and 14 | 1316 |
| 177 and 118 | 354 |