Least Common Multiple (LCM) of 127 and 77
The least common multiple (LCM) of 127 and 77 is 9779.
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 127 and 77?
First, calculate the GCD of 127 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 77 = 1 remainder 50 |
| 2 | 77 ÷ 50 = 1 remainder 27 |
| 3 | 50 ÷ 27 = 1 remainder 23 |
| 4 | 27 ÷ 23 = 1 remainder 4 |
| 5 | 23 ÷ 4 = 5 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 121 | 7139 |
| 80 and 126 | 5040 |
| 186 and 102 | 3162 |
| 109 and 18 | 1962 |
| 141 and 195 | 9165 |