Least Common Multiple (LCM) of 159 and 117
The least common multiple (LCM) of 159 and 117 is 6201.
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 117?
First, calculate the GCD of 159 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 117 = 1 remainder 42 |
| 2 | 117 ÷ 42 = 2 remainder 33 |
| 3 | 42 ÷ 33 = 1 remainder 9 |
| 4 | 33 ÷ 9 = 3 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 43 | 7611 |
| 13 and 13 | 13 |
| 107 and 22 | 2354 |
| 197 and 200 | 39400 |
| 55 and 135 | 1485 |