Least Common Multiple (LCM) of 67 and 85
The least common multiple (LCM) of 67 and 85 is 5695.
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 85?
First, calculate the GCD of 67 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 85 = 0 remainder 67 |
| 2 | 85 ÷ 67 = 1 remainder 18 |
| 3 | 67 ÷ 18 = 3 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 104 | 6968 |
| 195 and 95 | 3705 |
| 32 and 37 | 1184 |
| 87 and 37 | 3219 |
| 187 and 28 | 5236 |