Least Common Multiple (LCM) of 61 and 77
The least common multiple (LCM) of 61 and 77 is 4697.
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 77?
First, calculate the GCD of 61 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 77 = 0 remainder 61 |
| 2 | 77 ÷ 61 = 1 remainder 16 |
| 3 | 61 ÷ 16 = 3 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 |
|---|---|
| 193 and 24 | 4632 |
| 64 and 103 | 6592 |
| 21 and 167 | 3507 |
| 97 and 197 | 19109 |
| 102 and 74 | 3774 |