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 |
|---|---|
| 36 and 27 | 108 |
| 86 and 189 | 16254 |
| 138 and 126 | 2898 |
| 36 and 102 | 612 |
| 99 and 158 | 15642 |