Least Common Multiple (LCM) of 45 and 103
The least common multiple (LCM) of 45 and 103 is 4635.
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 45 and 103?
First, calculate the GCD of 45 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 103 = 0 remainder 45 |
| 2 | 103 ÷ 45 = 2 remainder 13 |
| 3 | 45 ÷ 13 = 3 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 29 | 3973 |
| 15 and 82 | 1230 |
| 157 and 130 | 20410 |
| 178 and 18 | 1602 |
| 42 and 175 | 1050 |