Least Common Multiple (LCM) of 45 and 49
The least common multiple (LCM) of 45 and 49 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 45 and 49?
First, calculate the GCD of 45 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 49 = 0 remainder 45 |
| 2 | 49 ÷ 45 = 1 remainder 4 |
| 3 | 45 ÷ 4 = 11 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 117 | 1989 |
| 114 and 68 | 3876 |
| 85 and 44 | 3740 |
| 168 and 55 | 9240 |
| 181 and 83 | 15023 |