Least Common Multiple (LCM) of 17 and 79
The least common multiple (LCM) of 17 and 79 is 1343.
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 79?
First, calculate the GCD of 17 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 79 = 0 remainder 17 |
| 2 | 79 ÷ 17 = 4 remainder 11 |
| 3 | 17 ÷ 11 = 1 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 78 | 702 |
| 142 and 24 | 1704 |
| 120 and 191 | 22920 |
| 189 and 70 | 1890 |
| 51 and 72 | 1224 |