Least Common Multiple (LCM) of 103 and 191
The least common multiple (LCM) of 103 and 191 is 19673.
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 191?
First, calculate the GCD of 103 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 191 = 0 remainder 103 |
| 2 | 191 ÷ 103 = 1 remainder 88 |
| 3 | 103 ÷ 88 = 1 remainder 15 |
| 4 | 88 ÷ 15 = 5 remainder 13 |
| 5 | 15 ÷ 13 = 1 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 124 | 13764 |
| 108 and 45 | 540 |
| 86 and 70 | 3010 |
| 64 and 161 | 10304 |
| 126 and 94 | 5922 |