Least Common Multiple (LCM) of 61 and 107
The least common multiple (LCM) of 61 and 107 is 6527.
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 61 and 107?
First, calculate the GCD of 61 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 107 = 0 remainder 61 |
| 2 | 107 ÷ 61 = 1 remainder 46 |
| 3 | 61 ÷ 46 = 1 remainder 15 |
| 4 | 46 ÷ 15 = 3 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 82 | 6806 |
| 133 and 26 | 3458 |
| 134 and 37 | 4958 |
| 10 and 105 | 210 |
| 80 and 39 | 3120 |