Least Common Multiple (LCM) of 38 and 107
The least common multiple (LCM) of 38 and 107 is 4066.
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 38 and 107?
First, calculate the GCD of 38 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 107 = 0 remainder 38 |
| 2 | 107 ÷ 38 = 2 remainder 31 |
| 3 | 38 ÷ 31 = 1 remainder 7 |
| 4 | 31 ÷ 7 = 4 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 38 | 760 |
| 180 and 96 | 1440 |
| 169 and 137 | 23153 |
| 199 and 170 | 33830 |
| 93 and 127 | 11811 |