Least Common Multiple (LCM) of 89 and 115
The least common multiple (LCM) of 89 and 115 is 10235.
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 115?
First, calculate the GCD of 89 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 115 = 0 remainder 89 |
| 2 | 115 ÷ 89 = 1 remainder 26 |
| 3 | 89 ÷ 26 = 3 remainder 11 |
| 4 | 26 ÷ 11 = 2 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 145 | 8265 |
| 127 and 29 | 3683 |
| 24 and 73 | 1752 |
| 172 and 180 | 7740 |
| 25 and 151 | 3775 |