Least Common Multiple (LCM) of 38 and 83
The least common multiple (LCM) of 38 and 83 is 3154.
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 83?
First, calculate the GCD of 38 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 83 = 0 remainder 38 |
| 2 | 83 ÷ 38 = 2 remainder 7 |
| 3 | 38 ÷ 7 = 5 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 35 | 105 |
| 126 and 39 | 1638 |
| 190 and 63 | 11970 |
| 122 and 87 | 10614 |
| 169 and 10 | 1690 |