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 |
|---|---|
| 83 and 200 | 16600 |
| 117 and 152 | 17784 |
| 131 and 133 | 17423 |
| 24 and 121 | 2904 |
| 120 and 47 | 5640 |