Least Common Multiple (LCM) of 107 and 138
The least common multiple (LCM) of 107 and 138 is 14766.
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 138?
First, calculate the GCD of 107 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 138 = 0 remainder 107 |
| 2 | 138 ÷ 107 = 1 remainder 31 |
| 3 | 107 ÷ 31 = 3 remainder 14 |
| 4 | 31 ÷ 14 = 2 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 42 | 3570 |
| 47 and 23 | 1081 |
| 134 and 107 | 14338 |
| 154 and 137 | 21098 |
| 107 and 107 | 107 |