Least Common Multiple (LCM) of 122 and 174
The least common multiple (LCM) of 122 and 174 is 10614.
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 122 and 174?
First, calculate the GCD of 122 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 174 = 0 remainder 122 |
| 2 | 174 ÷ 122 = 1 remainder 52 |
| 3 | 122 ÷ 52 = 2 remainder 18 |
| 4 | 52 ÷ 18 = 2 remainder 16 |
| 5 | 18 ÷ 16 = 1 remainder 2 |
| 6 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 17 | 357 |
| 165 and 23 | 3795 |
| 75 and 143 | 10725 |
| 196 and 194 | 19012 |
| 58 and 173 | 10034 |