Least Common Multiple (LCM) of 49 and 45
The least common multiple (LCM) of 49 and 45 is 2205.
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 49 and 45?
First, calculate the GCD of 49 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 45 = 1 remainder 4 |
| 2 | 45 ÷ 4 = 11 remainder 1 |
| 3 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 103 | 12257 |
| 193 and 183 | 35319 |
| 63 and 128 | 8064 |
| 183 and 83 | 15189 |
| 34 and 116 | 1972 |