Least Common Multiple (LCM) of 22 and 102
The least common multiple (LCM) of 22 and 102 is 1122.
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 102?
First, calculate the GCD of 22 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 102 = 0 remainder 22 |
| 2 | 102 ÷ 22 = 4 remainder 14 |
| 3 | 22 ÷ 14 = 1 remainder 8 |
| 4 | 14 ÷ 8 = 1 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 68 | 884 |
| 180 and 174 | 5220 |
| 140 and 30 | 420 |
| 43 and 152 | 6536 |
| 179 and 55 | 9845 |