Least Common Multiple (LCM) of 106 and 118
The least common multiple (LCM) of 106 and 118 is 6254.
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 118?
First, calculate the GCD of 106 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 118 = 0 remainder 106 |
| 2 | 118 ÷ 106 = 1 remainder 12 |
| 3 | 106 ÷ 12 = 8 remainder 10 |
| 4 | 12 ÷ 10 = 1 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 200 | 2200 |
| 157 and 13 | 2041 |
| 194 and 31 | 6014 |
| 68 and 103 | 7004 |
| 105 and 186 | 6510 |