Least Common Multiple (LCM) of 159 and 123
The least common multiple (LCM) of 159 and 123 is 6519.
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 159 and 123?
First, calculate the GCD of 159 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 123 = 1 remainder 36 |
| 2 | 123 ÷ 36 = 3 remainder 15 |
| 3 | 36 ÷ 15 = 2 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 98 | 13230 |
| 20 and 131 | 2620 |
| 115 and 196 | 22540 |
| 109 and 123 | 13407 |
| 42 and 109 | 4578 |