Least Common Multiple (LCM) of 22 and 109
The least common multiple (LCM) of 22 and 109 is 2398.
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 109?
First, calculate the GCD of 22 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 109 = 0 remainder 22 |
| 2 | 109 ÷ 22 = 4 remainder 21 |
| 3 | 22 ÷ 21 = 1 remainder 1 |
| 4 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 27 | 3294 |
| 139 and 120 | 16680 |
| 116 and 51 | 5916 |
| 33 and 132 | 132 |
| 144 and 105 | 5040 |