Least Common Multiple (LCM) of 97 and 122
The least common multiple (LCM) of 97 and 122 is 11834.
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 97 and 122?
First, calculate the GCD of 97 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 122 = 0 remainder 97 |
| 2 | 122 ÷ 97 = 1 remainder 25 |
| 3 | 97 ÷ 25 = 3 remainder 22 |
| 4 | 25 ÷ 22 = 1 remainder 3 |
| 5 | 22 ÷ 3 = 7 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 53 | 7049 |
| 75 and 189 | 4725 |
| 193 and 172 | 33196 |
| 33 and 164 | 5412 |
| 185 and 171 | 31635 |