Least Common Multiple (LCM) of 110 and 103
The least common multiple (LCM) of 110 and 103 is 11330.
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 110 and 103?
First, calculate the GCD of 110 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 103 = 1 remainder 7 |
| 2 | 103 ÷ 7 = 14 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 30 | 1050 |
| 54 and 130 | 3510 |
| 118 and 89 | 10502 |
| 122 and 162 | 9882 |
| 115 and 62 | 7130 |