Least Common Multiple (LCM) of 83 and 158
The least common multiple (LCM) of 83 and 158 is 13114.
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 158?
First, calculate the GCD of 83 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 158 = 0 remainder 83 |
| 2 | 158 ÷ 83 = 1 remainder 75 |
| 3 | 83 ÷ 75 = 1 remainder 8 |
| 4 | 75 ÷ 8 = 9 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 80 | 560 |
| 43 and 189 | 8127 |
| 43 and 142 | 6106 |
| 185 and 84 | 15540 |
| 109 and 185 | 20165 |