Least Common Multiple (LCM) of 114 and 69
The least common multiple (LCM) of 114 and 69 is 2622.
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 69?
First, calculate the GCD of 114 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 69 = 1 remainder 45 |
| 2 | 69 ÷ 45 = 1 remainder 24 |
| 3 | 45 ÷ 24 = 1 remainder 21 |
| 4 | 24 ÷ 21 = 1 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 63 | 315 |
| 101 and 31 | 3131 |
| 163 and 176 | 28688 |
| 12 and 48 | 48 |
| 11 and 143 | 143 |