Least Common Multiple (LCM) of 63 and 114
The least common multiple (LCM) of 63 and 114 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 63 and 114?
First, calculate the GCD of 63 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 114 = 0 remainder 63 |
| 2 | 114 ÷ 63 = 1 remainder 51 |
| 3 | 63 ÷ 51 = 1 remainder 12 |
| 4 | 51 ÷ 12 = 4 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 163 | 31459 |
| 174 and 160 | 13920 |
| 105 and 35 | 105 |
| 103 and 77 | 7931 |
| 24 and 89 | 2136 |