Least Common Multiple (LCM) of 109 and 22
The least common multiple (LCM) of 109 and 22 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 109 and 22?
First, calculate the GCD of 109 and 22 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 22 = 4 remainder 21 |
| 2 | 22 ÷ 21 = 1 remainder 1 |
| 3 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 75 | 150 |
| 131 and 69 | 9039 |
| 39 and 159 | 2067 |
| 145 and 164 | 23780 |
| 81 and 58 | 4698 |