Least Common Multiple (LCM) of 101 and 159
The least common multiple (LCM) of 101 and 159 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 101 and 159?
First, calculate the GCD of 101 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 159 = 0 remainder 101 |
| 2 | 159 ÷ 101 = 1 remainder 58 |
| 3 | 101 ÷ 58 = 1 remainder 43 |
| 4 | 58 ÷ 43 = 1 remainder 15 |
| 5 | 43 ÷ 15 = 2 remainder 13 |
| 6 | 15 ÷ 13 = 1 remainder 2 |
| 7 | 13 ÷ 2 = 6 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 132 | 1716 |
| 80 and 122 | 4880 |
| 60 and 64 | 960 |
| 197 and 95 | 18715 |
| 86 and 160 | 6880 |