Least Common Multiple (LCM) of 114 and 77
The least common multiple (LCM) of 114 and 77 is 8778.
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 114 and 77?
First, calculate the GCD of 114 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 77 = 1 remainder 37 |
| 2 | 77 ÷ 37 = 2 remainder 3 |
| 3 | 37 ÷ 3 = 12 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 161 | 23506 |
| 170 and 71 | 12070 |
| 90 and 105 | 630 |
| 12 and 86 | 516 |
| 70 and 91 | 910 |