Least Common Multiple (LCM) of 138 and 109
The least common multiple (LCM) of 138 and 109 is 15042.
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 109?
First, calculate the GCD of 138 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 109 = 1 remainder 29 |
| 2 | 109 ÷ 29 = 3 remainder 22 |
| 3 | 29 ÷ 22 = 1 remainder 7 |
| 4 | 22 ÷ 7 = 3 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 40 | 1480 |
| 182 and 53 | 9646 |
| 89 and 153 | 13617 |
| 117 and 195 | 585 |
| 76 and 188 | 3572 |