Least Common Multiple (LCM) of 17 and 73
The least common multiple (LCM) of 17 and 73 is 1241.
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 73?
First, calculate the GCD of 17 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 73 = 0 remainder 17 |
| 2 | 73 ÷ 17 = 4 remainder 5 |
| 3 | 17 ÷ 5 = 3 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 113 | 17967 |
| 11 and 100 | 1100 |
| 176 and 55 | 880 |
| 193 and 139 | 26827 |
| 115 and 125 | 2875 |