Least Common Multiple (LCM) of 123 and 170
The least common multiple (LCM) of 123 and 170 is 20910.
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 123 and 170?
First, calculate the GCD of 123 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 170 = 0 remainder 123 |
| 2 | 170 ÷ 123 = 1 remainder 47 |
| 3 | 123 ÷ 47 = 2 remainder 29 |
| 4 | 47 ÷ 29 = 1 remainder 18 |
| 5 | 29 ÷ 18 = 1 remainder 11 |
| 6 | 18 ÷ 11 = 1 remainder 7 |
| 7 | 11 ÷ 7 = 1 remainder 4 |
| 8 | 7 ÷ 4 = 1 remainder 3 |
| 9 | 4 ÷ 3 = 1 remainder 1 |
| 10 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 11 | 1529 |
| 137 and 31 | 4247 |
| 177 and 42 | 2478 |
| 128 and 197 | 25216 |
| 36 and 135 | 540 |