Least Common Multiple (LCM) of 22 and 123
The least common multiple (LCM) of 22 and 123 is 2706.
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 123?
First, calculate the GCD of 22 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 123 = 0 remainder 22 |
| 2 | 123 ÷ 22 = 5 remainder 13 |
| 3 | 22 ÷ 13 = 1 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 63 | 3339 |
| 176 and 74 | 6512 |
| 107 and 22 | 2354 |
| 176 and 104 | 2288 |
| 11 and 14 | 154 |