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 |
|---|---|
| 13 and 146 | 1898 |
| 103 and 102 | 10506 |
| 104 and 66 | 3432 |
| 86 and 143 | 12298 |
| 141 and 12 | 564 |