Least Common Multiple (LCM) of 159 and 101
The least common multiple (LCM) of 159 and 101 is 16059.
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 101?
First, calculate the GCD of 159 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 101 = 1 remainder 58 |
| 2 | 101 ÷ 58 = 1 remainder 43 |
| 3 | 58 ÷ 43 = 1 remainder 15 |
| 4 | 43 ÷ 15 = 2 remainder 13 |
| 5 | 15 ÷ 13 = 1 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 34 | 6698 |
| 25 and 49 | 1225 |
| 122 and 67 | 8174 |
| 135 and 135 | 135 |
| 153 and 44 | 6732 |