Least Common Multiple (LCM) of 83 and 115
The least common multiple (LCM) of 83 and 115 is 9545.
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 83 and 115?
First, calculate the GCD of 83 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 115 = 0 remainder 83 |
| 2 | 115 ÷ 83 = 1 remainder 32 |
| 3 | 83 ÷ 32 = 2 remainder 19 |
| 4 | 32 ÷ 19 = 1 remainder 13 |
| 5 | 19 ÷ 13 = 1 remainder 6 |
| 6 | 13 ÷ 6 = 2 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 199 | 21293 |
| 122 and 28 | 1708 |
| 151 and 63 | 9513 |
| 30 and 160 | 480 |
| 160 and 29 | 4640 |