Least Common Multiple (LCM) of 51 and 77
The least common multiple (LCM) of 51 and 77 is 3927.
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 51 and 77?
First, calculate the GCD of 51 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 77 = 0 remainder 51 |
| 2 | 77 ÷ 51 = 1 remainder 26 |
| 3 | 51 ÷ 26 = 1 remainder 25 |
| 4 | 26 ÷ 25 = 1 remainder 1 |
| 5 | 25 ÷ 1 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 96 | 5088 |
| 34 and 98 | 1666 |
| 127 and 185 | 23495 |
| 17 and 116 | 1972 |
| 38 and 51 | 1938 |