Least Common Multiple (LCM) of 137 and 159
The least common multiple (LCM) of 137 and 159 is 21783.
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 137 and 159?
First, calculate the GCD of 137 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 159 = 0 remainder 137 |
| 2 | 159 ÷ 137 = 1 remainder 22 |
| 3 | 137 ÷ 22 = 6 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 42 | 546 |
| 37 and 106 | 3922 |
| 140 and 25 | 700 |
| 112 and 166 | 9296 |
| 49 and 55 | 2695 |