Least Common Multiple (LCM) of 38 and 67
The least common multiple (LCM) of 38 and 67 is 2546.
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 67?
First, calculate the GCD of 38 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 67 = 0 remainder 38 |
| 2 | 67 ÷ 38 = 1 remainder 29 |
| 3 | 38 ÷ 29 = 1 remainder 9 |
| 4 | 29 ÷ 9 = 3 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 149 | 12218 |
| 80 and 63 | 5040 |
| 161 and 157 | 25277 |
| 54 and 39 | 702 |
| 44 and 31 | 1364 |