Least Common Multiple (LCM) of 123 and 171
The least common multiple (LCM) of 123 and 171 is 7011.
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 171?
First, calculate the GCD of 123 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 171 = 0 remainder 123 |
| 2 | 171 ÷ 123 = 1 remainder 48 |
| 3 | 123 ÷ 48 = 2 remainder 27 |
| 4 | 48 ÷ 27 = 1 remainder 21 |
| 5 | 27 ÷ 21 = 1 remainder 6 |
| 6 | 21 ÷ 6 = 3 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 164 | 5904 |
| 23 and 65 | 1495 |
| 40 and 101 | 4040 |
| 113 and 144 | 16272 |
| 155 and 124 | 620 |