Least Common Multiple (LCM) of 106 and 160
The least common multiple (LCM) of 106 and 160 is 8480.
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 160?
First, calculate the GCD of 106 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 160 = 0 remainder 106 |
| 2 | 160 ÷ 106 = 1 remainder 54 |
| 3 | 106 ÷ 54 = 1 remainder 52 |
| 4 | 54 ÷ 52 = 1 remainder 2 |
| 5 | 52 ÷ 2 = 26 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 198 | 11088 |
| 83 and 100 | 8300 |
| 58 and 36 | 1044 |
| 125 and 159 | 19875 |
| 189 and 160 | 30240 |