Least Common Multiple (LCM) of 101 and 114
The least common multiple (LCM) of 101 and 114 is 11514.
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 114?
First, calculate the GCD of 101 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 114 = 0 remainder 101 |
| 2 | 114 ÷ 101 = 1 remainder 13 |
| 3 | 101 ÷ 13 = 7 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 14 | 1316 |
| 198 and 97 | 19206 |
| 49 and 189 | 1323 |
| 110 and 197 | 21670 |
| 50 and 135 | 1350 |