Least Common Multiple (LCM) of 114 and 54
The least common multiple (LCM) of 114 and 54 is 1026.
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 54?
First, calculate the GCD of 114 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 54 = 2 remainder 6 |
| 2 | 54 ÷ 6 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 189 | 4347 |
| 120 and 159 | 6360 |
| 52 and 172 | 2236 |
| 110 and 117 | 12870 |
| 39 and 17 | 663 |