Least Common Multiple (LCM) of 123 and 159
The least common multiple (LCM) of 123 and 159 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 123 and 159?
First, calculate the GCD of 123 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 159 = 0 remainder 123 |
| 2 | 159 ÷ 123 = 1 remainder 36 |
| 3 | 123 ÷ 36 = 3 remainder 15 |
| 4 | 36 ÷ 15 = 2 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 183 | 5307 |
| 88 and 160 | 1760 |
| 76 and 149 | 11324 |
| 138 and 83 | 11454 |
| 146 and 151 | 22046 |