Least Common Multiple (LCM) of 89 and 137
The least common multiple (LCM) of 89 and 137 is 12193.
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 137?
First, calculate the GCD of 89 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 137 = 0 remainder 89 |
| 2 | 137 ÷ 89 = 1 remainder 48 |
| 3 | 89 ÷ 48 = 1 remainder 41 |
| 4 | 48 ÷ 41 = 1 remainder 7 |
| 5 | 41 ÷ 7 = 5 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 115 | 4140 |
| 192 and 198 | 6336 |
| 96 and 52 | 1248 |
| 161 and 56 | 1288 |
| 39 and 27 | 351 |