Least Common Multiple (LCM) of 69 and 114
The least common multiple (LCM) of 69 and 114 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 69 and 114?
First, calculate the GCD of 69 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 114 = 0 remainder 69 |
| 2 | 114 ÷ 69 = 1 remainder 45 |
| 3 | 69 ÷ 45 = 1 remainder 24 |
| 4 | 45 ÷ 24 = 1 remainder 21 |
| 5 | 24 ÷ 21 = 1 remainder 3 |
| 6 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 126 | 12600 |
| 61 and 82 | 5002 |
| 83 and 187 | 15521 |
| 15 and 131 | 1965 |
| 163 and 25 | 4075 |