Least Common Multiple (LCM) of 114 and 17
The least common multiple (LCM) of 114 and 17 is 1938.
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 114 and 17?
First, calculate the GCD of 114 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 17 = 6 remainder 12 |
| 2 | 17 ÷ 12 = 1 remainder 5 |
| 3 | 12 ÷ 5 = 2 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 134 | 2814 |
| 84 and 75 | 2100 |
| 130 and 51 | 6630 |
| 158 and 167 | 26386 |
| 15 and 135 | 135 |