Least Common Multiple (LCM) of 89 and 138
The least common multiple (LCM) of 89 and 138 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 89 and 138?
First, calculate the GCD of 89 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 138 = 0 remainder 89 |
| 2 | 138 ÷ 89 = 1 remainder 49 |
| 3 | 89 ÷ 49 = 1 remainder 40 |
| 4 | 49 ÷ 40 = 1 remainder 9 |
| 5 | 40 ÷ 9 = 4 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 120 | 11640 |
| 69 and 155 | 10695 |
| 191 and 74 | 14134 |
| 27 and 134 | 3618 |
| 121 and 67 | 8107 |