Least Common Multiple (LCM) of 67 and 95
The least common multiple (LCM) of 67 and 95 is 6365.
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 95?
First, calculate the GCD of 67 and 95 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 95 = 0 remainder 67 |
| 2 | 95 ÷ 67 = 1 remainder 28 |
| 3 | 67 ÷ 28 = 2 remainder 11 |
| 4 | 28 ÷ 11 = 2 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 199 | 32238 |
| 166 and 175 | 29050 |
| 70 and 160 | 1120 |
| 82 and 64 | 2624 |
| 142 and 116 | 8236 |