Least Common Multiple (LCM) of 171 and 123
The least common multiple (LCM) of 171 and 123 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 171 and 123?
First, calculate the GCD of 171 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 171 ÷ 123 = 1 remainder 48 |
| 2 | 123 ÷ 48 = 2 remainder 27 |
| 3 | 48 ÷ 27 = 1 remainder 21 |
| 4 | 27 ÷ 21 = 1 remainder 6 |
| 5 | 21 ÷ 6 = 3 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 132 | 924 |
| 70 and 20 | 140 |
| 85 and 30 | 510 |
| 164 and 86 | 7052 |
| 141 and 36 | 1692 |