Least Common Multiple (LCM) of 45 and 107
The least common multiple (LCM) of 45 and 107 is 4815.
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 107?
First, calculate the GCD of 45 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 107 = 0 remainder 45 |
| 2 | 107 ÷ 45 = 2 remainder 17 |
| 3 | 45 ÷ 17 = 2 remainder 11 |
| 4 | 17 ÷ 11 = 1 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 17 | 238 |
| 80 and 183 | 14640 |
| 46 and 85 | 3910 |
| 107 and 157 | 16799 |
| 110 and 111 | 12210 |