Least Common Multiple (LCM) of 45 and 61
The least common multiple (LCM) of 45 and 61 is 2745.
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 61?
First, calculate the GCD of 45 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 61 = 0 remainder 45 |
| 2 | 61 ÷ 45 = 1 remainder 16 |
| 3 | 45 ÷ 16 = 2 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 120 | 1560 |
| 47 and 161 | 7567 |
| 101 and 163 | 16463 |
| 160 and 42 | 3360 |
| 167 and 14 | 2338 |