Least Common Multiple (LCM) of 103 and 172
The least common multiple (LCM) of 103 and 172 is 17716.
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 172?
First, calculate the GCD of 103 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 172 = 0 remainder 103 |
| 2 | 172 ÷ 103 = 1 remainder 69 |
| 3 | 103 ÷ 69 = 1 remainder 34 |
| 4 | 69 ÷ 34 = 2 remainder 1 |
| 5 | 34 ÷ 1 = 34 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 137 | 1644 |
| 192 and 192 | 192 |
| 200 and 53 | 10600 |
| 46 and 68 | 1564 |
| 52 and 137 | 7124 |