Least Common Multiple (LCM) of 51 and 114
The least common multiple (LCM) of 51 and 114 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 51 and 114?
First, calculate the GCD of 51 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 114 = 0 remainder 51 |
| 2 | 114 ÷ 51 = 2 remainder 12 |
| 3 | 51 ÷ 12 = 4 remainder 3 |
| 4 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 66 | 2838 |
| 140 and 16 | 560 |
| 190 and 186 | 17670 |
| 164 and 62 | 5084 |
| 189 and 75 | 4725 |