Least Common Multiple (LCM) of 138 and 159
The least common multiple (LCM) of 138 and 159 is 7314.
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 138 and 159?
First, calculate the GCD of 138 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 159 = 0 remainder 138 |
| 2 | 159 ÷ 138 = 1 remainder 21 |
| 3 | 138 ÷ 21 = 6 remainder 12 |
| 4 | 21 ÷ 12 = 1 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 42 | 966 |
| 140 and 196 | 980 |
| 106 and 37 | 3922 |
| 59 and 199 | 11741 |
| 81 and 106 | 8586 |