Least Common Multiple (LCM) of 106 and 191
The least common multiple (LCM) of 106 and 191 is 20246.
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 191?
First, calculate the GCD of 106 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 191 = 0 remainder 106 |
| 2 | 191 ÷ 106 = 1 remainder 85 |
| 3 | 106 ÷ 85 = 1 remainder 21 |
| 4 | 85 ÷ 21 = 4 remainder 1 |
| 5 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 117 | 3393 |
| 40 and 42 | 840 |
| 35 and 132 | 4620 |
| 165 and 138 | 7590 |
| 17 and 56 | 952 |