Least Common Multiple (LCM) of 107 and 22
The least common multiple (LCM) of 107 and 22 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 107 and 22?
First, calculate the GCD of 107 and 22 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 22 = 4 remainder 19 |
| 2 | 22 ÷ 19 = 1 remainder 3 |
| 3 | 19 ÷ 3 = 6 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 13 | 1781 |
| 174 and 97 | 16878 |
| 122 and 197 | 24034 |
| 62 and 85 | 5270 |
| 199 and 105 | 20895 |