Least Common Multiple (LCM) of 138 and 89
The least common multiple (LCM) of 138 and 89 is 12282.
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 89?
First, calculate the GCD of 138 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 89 = 1 remainder 49 |
| 2 | 89 ÷ 49 = 1 remainder 40 |
| 3 | 49 ÷ 40 = 1 remainder 9 |
| 4 | 40 ÷ 9 = 4 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 44 | 176 |
| 109 and 172 | 18748 |
| 36 and 66 | 396 |
| 198 and 33 | 198 |
| 118 and 109 | 12862 |