Least Common Multiple (LCM) of 103 and 167
The least common multiple (LCM) of 103 and 167 is 17201.
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 167?
First, calculate the GCD of 103 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 167 = 0 remainder 103 |
| 2 | 167 ÷ 103 = 1 remainder 64 |
| 3 | 103 ÷ 64 = 1 remainder 39 |
| 4 | 64 ÷ 39 = 1 remainder 25 |
| 5 | 39 ÷ 25 = 1 remainder 14 |
| 6 | 25 ÷ 14 = 1 remainder 11 |
| 7 | 14 ÷ 11 = 1 remainder 3 |
| 8 | 11 ÷ 3 = 3 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 24 | 4440 |
| 105 and 178 | 18690 |
| 115 and 165 | 3795 |
| 50 and 141 | 7050 |
| 129 and 27 | 1161 |