Least Common Multiple (LCM) of 12 and 17
The least common multiple (LCM) of 12 and 17 is 204.
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 12 and 17?
First, calculate the GCD of 12 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 17 = 0 remainder 12 |
| 2 | 17 ÷ 12 = 1 remainder 5 |
| 3 | 12 ÷ 5 = 2 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 124 | 17980 |
| 184 and 124 | 5704 |
| 187 and 160 | 29920 |
| 119 and 164 | 19516 |
| 184 and 32 | 736 |