Least Common Multiple (LCM) of 172 and 122
The least common multiple (LCM) of 172 and 122 is 10492.
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 172 and 122?
First, calculate the GCD of 172 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 122 = 1 remainder 50 |
| 2 | 122 ÷ 50 = 2 remainder 22 |
| 3 | 50 ÷ 22 = 2 remainder 6 |
| 4 | 22 ÷ 6 = 3 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 53 | 7261 |
| 10 and 86 | 430 |
| 151 and 67 | 10117 |
| 54 and 29 | 1566 |
| 194 and 50 | 4850 |