Least Common Multiple (LCM) of 106 and 83
The least common multiple (LCM) of 106 and 83 is 8798.
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 106 and 83?
First, calculate the GCD of 106 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 83 = 1 remainder 23 |
| 2 | 83 ÷ 23 = 3 remainder 14 |
| 3 | 23 ÷ 14 = 1 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 167 | 11523 |
| 168 and 105 | 840 |
| 105 and 140 | 420 |
| 68 and 53 | 3604 |
| 181 and 151 | 27331 |