Least Common Multiple (LCM) of 138 and 74
The least common multiple (LCM) of 138 and 74 is 5106.
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 138 and 74?
First, calculate the GCD of 138 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 74 = 1 remainder 64 |
| 2 | 74 ÷ 64 = 1 remainder 10 |
| 3 | 64 ÷ 10 = 6 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 105 | 3045 |
| 64 and 197 | 12608 |
| 46 and 28 | 644 |
| 43 and 153 | 6579 |
| 24 and 179 | 4296 |