Least Common Multiple (LCM) of 22 and 126
The least common multiple (LCM) of 22 and 126 is 1386.
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 126?
First, calculate the GCD of 22 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 126 = 0 remainder 22 |
| 2 | 126 ÷ 22 = 5 remainder 16 |
| 3 | 22 ÷ 16 = 1 remainder 6 |
| 4 | 16 ÷ 6 = 2 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 77 | 385 |
| 177 and 65 | 11505 |
| 138 and 19 | 2622 |
| 194 and 21 | 4074 |
| 173 and 57 | 9861 |