Least Common Multiple (LCM) of 61 and 65
The least common multiple (LCM) of 61 and 65 is 3965.
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 65?
First, calculate the GCD of 61 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 65 = 0 remainder 61 |
| 2 | 65 ÷ 61 = 1 remainder 4 |
| 3 | 61 ÷ 4 = 15 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 86 | 1290 |
| 61 and 200 | 12200 |
| 105 and 62 | 6510 |
| 157 and 36 | 5652 |
| 128 and 11 | 1408 |