Least Common Multiple (LCM) of 170 and 103
The least common multiple (LCM) of 170 and 103 is 17510.
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 170 and 103?
First, calculate the GCD of 170 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 103 = 1 remainder 67 |
| 2 | 103 ÷ 67 = 1 remainder 36 |
| 3 | 67 ÷ 36 = 1 remainder 31 |
| 4 | 36 ÷ 31 = 1 remainder 5 |
| 5 | 31 ÷ 5 = 6 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 100 | 9900 |
| 135 and 186 | 8370 |
| 91 and 75 | 6825 |
| 25 and 78 | 1950 |
| 145 and 76 | 11020 |