Least Common Multiple (LCM) of 89 and 103
The least common multiple (LCM) of 89 and 103 is 9167.
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 103?
First, calculate the GCD of 89 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 103 = 0 remainder 89 |
| 2 | 103 ÷ 89 = 1 remainder 14 |
| 3 | 89 ÷ 14 = 6 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 70 | 3080 |
| 58 and 190 | 5510 |
| 120 and 11 | 1320 |
| 67 and 13 | 871 |
| 141 and 115 | 16215 |