Least Common Multiple (LCM) of 67 and 55
The least common multiple (LCM) of 67 and 55 is 3685.
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 55?
First, calculate the GCD of 67 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 55 = 1 remainder 12 |
| 2 | 55 ÷ 12 = 4 remainder 7 |
| 3 | 12 ÷ 7 = 1 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 104 | 2080 |
| 182 and 66 | 6006 |
| 101 and 183 | 18483 |
| 21 and 189 | 189 |
| 67 and 182 | 12194 |