Least Common Multiple (LCM) of 103 and 157
The least common multiple (LCM) of 103 and 157 is 16171.
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 157?
First, calculate the GCD of 103 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 157 = 0 remainder 103 |
| 2 | 157 ÷ 103 = 1 remainder 54 |
| 3 | 103 ÷ 54 = 1 remainder 49 |
| 4 | 54 ÷ 49 = 1 remainder 5 |
| 5 | 49 ÷ 5 = 9 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 107 | 1284 |
| 24 and 135 | 1080 |
| 34 and 132 | 2244 |
| 109 and 53 | 5777 |
| 31 and 198 | 6138 |