Least Common Multiple (LCM) of 159 and 116
The least common multiple (LCM) of 159 and 116 is 18444.
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 116?
First, calculate the GCD of 159 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 116 = 1 remainder 43 |
| 2 | 116 ÷ 43 = 2 remainder 30 |
| 3 | 43 ÷ 30 = 1 remainder 13 |
| 4 | 30 ÷ 13 = 2 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 18 | 1548 |
| 73 and 101 | 7373 |
| 193 and 154 | 29722 |
| 190 and 129 | 24510 |
| 49 and 48 | 2352 |