Least Common Multiple (LCM) of 17 and 67
The least common multiple (LCM) of 17 and 67 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 17 and 67?
First, calculate the GCD of 17 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 67 = 0 remainder 17 |
| 2 | 67 ÷ 17 = 3 remainder 16 |
| 3 | 17 ÷ 16 = 1 remainder 1 |
| 4 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 21 | 273 |
| 21 and 163 | 3423 |
| 122 and 20 | 1220 |
| 131 and 45 | 5895 |
| 140 and 22 | 1540 |