Least Common Multiple (LCM) of 106 and 22
The least common multiple (LCM) of 106 and 22 is 1166.
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 106 and 22?
First, calculate the GCD of 106 and 22 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 22 = 4 remainder 18 |
| 2 | 22 ÷ 18 = 1 remainder 4 |
| 3 | 18 ÷ 4 = 4 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 111 | 3441 |
| 46 and 25 | 1150 |
| 99 and 115 | 11385 |
| 169 and 41 | 6929 |
| 56 and 173 | 9688 |