Least Common Multiple (LCM) of 67 and 103
The least common multiple (LCM) of 67 and 103 is 6901.
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 103?
First, calculate the GCD of 67 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 103 = 0 remainder 67 |
| 2 | 103 ÷ 67 = 1 remainder 36 |
| 3 | 67 ÷ 36 = 1 remainder 31 |
| 4 | 36 ÷ 31 = 1 remainder 5 |
| 5 | 31 ÷ 5 = 6 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 74 | 7474 |
| 91 and 11 | 1001 |
| 125 and 61 | 7625 |
| 110 and 177 | 19470 |
| 30 and 173 | 5190 |