Least Common Multiple (LCM) of 103 and 188
The least common multiple (LCM) of 103 and 188 is 19364.
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 188?
First, calculate the GCD of 103 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 188 = 0 remainder 103 |
| 2 | 188 ÷ 103 = 1 remainder 85 |
| 3 | 103 ÷ 85 = 1 remainder 18 |
| 4 | 85 ÷ 18 = 4 remainder 13 |
| 5 | 18 ÷ 13 = 1 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 117 | 1170 |
| 69 and 160 | 11040 |
| 26 and 92 | 1196 |
| 53 and 117 | 6201 |
| 109 and 48 | 5232 |