Least Common Multiple (LCM) of 22 and 107
The least common multiple (LCM) of 22 and 107 is 2354.
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 107?
First, calculate the GCD of 22 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 107 = 0 remainder 22 |
| 2 | 107 ÷ 22 = 4 remainder 19 |
| 3 | 22 ÷ 19 = 1 remainder 3 |
| 4 | 19 ÷ 3 = 6 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 150 | 8700 |
| 160 and 141 | 22560 |
| 78 and 50 | 1950 |
| 20 and 109 | 2180 |
| 121 and 102 | 12342 |