Least Common Multiple (LCM) of 22 and 122
The least common multiple (LCM) of 22 and 122 is 1342.
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 122?
First, calculate the GCD of 22 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 122 = 0 remainder 22 |
| 2 | 122 ÷ 22 = 5 remainder 12 |
| 3 | 22 ÷ 12 = 1 remainder 10 |
| 4 | 12 ÷ 10 = 1 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 151 | 19026 |
| 75 and 113 | 8475 |
| 27 and 170 | 4590 |
| 131 and 140 | 18340 |
| 157 and 62 | 9734 |