Least Common Multiple (LCM) of 106 and 181
The least common multiple (LCM) of 106 and 181 is 19186.
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 181?
First, calculate the GCD of 106 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 181 = 0 remainder 106 |
| 2 | 181 ÷ 106 = 1 remainder 75 |
| 3 | 106 ÷ 75 = 1 remainder 31 |
| 4 | 75 ÷ 31 = 2 remainder 13 |
| 5 | 31 ÷ 13 = 2 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 19 | 2261 |
| 80 and 128 | 640 |
| 103 and 137 | 14111 |
| 102 and 71 | 7242 |
| 161 and 116 | 18676 |