Least Common Multiple (LCM) of 67 and 17
The least common multiple (LCM) of 67 and 17 is 1139.
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 17?
First, calculate the GCD of 67 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 17 = 3 remainder 16 |
| 2 | 17 ÷ 16 = 1 remainder 1 |
| 3 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 61 | 7503 |
| 115 and 99 | 11385 |
| 63 and 82 | 5166 |
| 198 and 127 | 25146 |
| 31 and 83 | 2573 |