Least Common Multiple (LCM) of 106 and 55
The least common multiple (LCM) of 106 and 55 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 106 and 55?
First, calculate the GCD of 106 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 55 = 1 remainder 51 |
| 2 | 55 ÷ 51 = 1 remainder 4 |
| 3 | 51 ÷ 4 = 12 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 187 | 2244 |
| 49 and 165 | 8085 |
| 109 and 111 | 12099 |
| 18 and 142 | 1278 |
| 146 and 115 | 16790 |