Least Common Multiple (LCM) of 101 and 131
The least common multiple (LCM) of 101 and 131 is 13231.
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 131?
First, calculate the GCD of 101 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 131 = 0 remainder 101 |
| 2 | 131 ÷ 101 = 1 remainder 30 |
| 3 | 101 ÷ 30 = 3 remainder 11 |
| 4 | 30 ÷ 11 = 2 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 115 | 17595 |
| 102 and 199 | 20298 |
| 48 and 154 | 3696 |
| 114 and 175 | 19950 |
| 189 and 183 | 11529 |