Least Common Multiple (LCM) of 122 and 170
The least common multiple (LCM) of 122 and 170 is 10370.
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 170?
First, calculate the GCD of 122 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 170 = 0 remainder 122 |
| 2 | 170 ÷ 122 = 1 remainder 48 |
| 3 | 122 ÷ 48 = 2 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 |
|---|---|
| 135 and 96 | 4320 |
| 22 and 119 | 2618 |
| 174 and 32 | 2784 |
| 30 and 83 | 2490 |
| 68 and 24 | 408 |