Least Common Multiple (LCM) of 55 and 106
The least common multiple (LCM) of 55 and 106 is 5830.
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 55 and 106?
First, calculate the GCD of 55 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 106 = 0 remainder 55 |
| 2 | 106 ÷ 55 = 1 remainder 51 |
| 3 | 55 ÷ 51 = 1 remainder 4 |
| 4 | 51 ÷ 4 = 12 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 166 | 12118 |
| 106 and 188 | 9964 |
| 18 and 49 | 882 |
| 35 and 196 | 980 |
| 176 and 197 | 34672 |