Least Common Multiple (LCM) of 108 and 103
The least common multiple (LCM) of 108 and 103 is 11124.
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 108 and 103?
First, calculate the GCD of 108 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 103 = 1 remainder 5 |
| 2 | 103 ÷ 5 = 20 remainder 3 |
| 3 | 5 ÷ 3 = 1 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 68 | 4556 |
| 200 and 102 | 10200 |
| 87 and 161 | 14007 |
| 127 and 132 | 16764 |
| 172 and 96 | 4128 |