Least Common Multiple (LCM) of 114 and 63
The least common multiple (LCM) of 114 and 63 is 2394.
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 63?
First, calculate the GCD of 114 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 63 = 1 remainder 51 |
| 2 | 63 ÷ 51 = 1 remainder 12 |
| 3 | 51 ÷ 12 = 4 remainder 3 |
| 4 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 193 | 36284 |
| 121 and 33 | 363 |
| 91 and 200 | 18200 |
| 17 and 16 | 272 |
| 105 and 50 | 1050 |