Least Common Multiple (LCM) of 67 and 115
The least common multiple (LCM) of 67 and 115 is 7705.
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 115?
First, calculate the GCD of 67 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 115 = 0 remainder 67 |
| 2 | 115 ÷ 67 = 1 remainder 48 |
| 3 | 67 ÷ 48 = 1 remainder 19 |
| 4 | 48 ÷ 19 = 2 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 71 | 9727 |
| 24 and 111 | 888 |
| 164 and 50 | 4100 |
| 195 and 19 | 3705 |
| 91 and 128 | 11648 |