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 |
|---|---|
| 144 and 125 | 18000 |
| 120 and 119 | 14280 |
| 111 and 81 | 2997 |
| 120 and 116 | 3480 |
| 58 and 123 | 7134 |