Least Common Multiple (LCM) of 106 and 190
The least common multiple (LCM) of 106 and 190 is 10070.
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 190?
First, calculate the GCD of 106 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 190 = 0 remainder 106 |
| 2 | 190 ÷ 106 = 1 remainder 84 |
| 3 | 106 ÷ 84 = 1 remainder 22 |
| 4 | 84 ÷ 22 = 3 remainder 18 |
| 5 | 22 ÷ 18 = 1 remainder 4 |
| 6 | 18 ÷ 4 = 4 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 187 | 22440 |
| 99 and 115 | 11385 |
| 42 and 128 | 2688 |
| 118 and 136 | 8024 |
| 31 and 96 | 2976 |