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 |
|---|---|
| 128 and 30 | 1920 |
| 109 and 98 | 10682 |
| 125 and 142 | 17750 |
| 145 and 168 | 24360 |
| 151 and 62 | 9362 |