Least Common Multiple (LCM) of 38 and 109
The least common multiple (LCM) of 38 and 109 is 4142.
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 109?
First, calculate the GCD of 38 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 109 = 0 remainder 38 |
| 2 | 109 ÷ 38 = 2 remainder 33 |
| 3 | 38 ÷ 33 = 1 remainder 5 |
| 4 | 33 ÷ 5 = 6 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 20 | 1740 |
| 54 and 14 | 378 |
| 172 and 41 | 7052 |
| 186 and 54 | 1674 |
| 90 and 109 | 9810 |