Least Common Multiple (LCM) of 103 and 170
The least common multiple (LCM) of 103 and 170 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 103 and 170?
First, calculate the GCD of 103 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 170 = 0 remainder 103 |
| 2 | 170 ÷ 103 = 1 remainder 67 |
| 3 | 103 ÷ 67 = 1 remainder 36 |
| 4 | 67 ÷ 36 = 1 remainder 31 |
| 5 | 36 ÷ 31 = 1 remainder 5 |
| 6 | 31 ÷ 5 = 6 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 71 | 8165 |
| 60 and 94 | 2820 |
| 42 and 175 | 1050 |
| 65 and 68 | 4420 |
| 49 and 38 | 1862 |