Least Common Multiple (LCM) of 22 and 103
The least common multiple (LCM) of 22 and 103 is 2266.
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 103?
First, calculate the GCD of 22 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 103 = 0 remainder 22 |
| 2 | 103 ÷ 22 = 4 remainder 15 |
| 3 | 22 ÷ 15 = 1 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 65 | 12480 |
| 151 and 150 | 22650 |
| 125 and 179 | 22375 |
| 139 and 63 | 8757 |
| 125 and 95 | 2375 |