Least Common Multiple (LCM) of 196 and 122
The least common multiple (LCM) of 196 and 122 is 11956.
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 196 and 122?
First, calculate the GCD of 196 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 122 = 1 remainder 74 |
| 2 | 122 ÷ 74 = 1 remainder 48 |
| 3 | 74 ÷ 48 = 1 remainder 26 |
| 4 | 48 ÷ 26 = 1 remainder 22 |
| 5 | 26 ÷ 22 = 1 remainder 4 |
| 6 | 22 ÷ 4 = 5 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 101 | 9292 |
| 19 and 89 | 1691 |
| 105 and 195 | 1365 |
| 56 and 72 | 504 |
| 57 and 177 | 3363 |