Least Common Multiple (LCM) of 170 and 123
The least common multiple (LCM) of 170 and 123 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 170 and 123?
First, calculate the GCD of 170 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 123 = 1 remainder 47 |
| 2 | 123 ÷ 47 = 2 remainder 29 |
| 3 | 47 ÷ 29 = 1 remainder 18 |
| 4 | 29 ÷ 18 = 1 remainder 11 |
| 5 | 18 ÷ 11 = 1 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 165 | 27060 |
| 97 and 190 | 18430 |
| 90 and 196 | 8820 |
| 129 and 85 | 10965 |
| 162 and 46 | 3726 |