Least Common Multiple (LCM) of 22 and 106
The least common multiple (LCM) of 22 and 106 is 1166.
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 22 and 106?
First, calculate the GCD of 22 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 106 = 0 remainder 22 |
| 2 | 106 ÷ 22 = 4 remainder 18 |
| 3 | 22 ÷ 18 = 1 remainder 4 |
| 4 | 18 ÷ 4 = 4 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 45 | 90 |
| 103 and 62 | 6386 |
| 196 and 59 | 11564 |
| 86 and 36 | 1548 |
| 61 and 105 | 6405 |