Least Common Multiple (LCM) of 67 and 127
The least common multiple (LCM) of 67 and 127 is 8509.
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 67 and 127?
First, calculate the GCD of 67 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 127 = 0 remainder 67 |
| 2 | 127 ÷ 67 = 1 remainder 60 |
| 3 | 67 ÷ 60 = 1 remainder 7 |
| 4 | 60 ÷ 7 = 8 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 115 | 15065 |
| 20 and 93 | 1860 |
| 127 and 121 | 15367 |
| 128 and 135 | 17280 |
| 96 and 98 | 4704 |