Least Common Multiple (LCM) of 83 and 146
The least common multiple (LCM) of 83 and 146 is 12118.
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 146?
First, calculate the GCD of 83 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 146 = 0 remainder 83 |
| 2 | 146 ÷ 83 = 1 remainder 63 |
| 3 | 83 ÷ 63 = 1 remainder 20 |
| 4 | 63 ÷ 20 = 3 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 45 | 4635 |
| 54 and 70 | 1890 |
| 87 and 85 | 7395 |
| 110 and 65 | 1430 |
| 63 and 138 | 2898 |