Least Common Multiple (LCM) of 69 and 127
The least common multiple (LCM) of 69 and 127 is 8763.
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 127?
First, calculate the GCD of 69 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 127 = 0 remainder 69 |
| 2 | 127 ÷ 69 = 1 remainder 58 |
| 3 | 69 ÷ 58 = 1 remainder 11 |
| 4 | 58 ÷ 11 = 5 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 188 | 28012 |
| 111 and 157 | 17427 |
| 122 and 170 | 10370 |
| 106 and 189 | 20034 |
| 71 and 116 | 8236 |