Least Common Multiple (LCM) of 77 and 117
The least common multiple (LCM) of 77 and 117 is 9009.
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 77 and 117?
First, calculate the GCD of 77 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 117 = 0 remainder 77 |
| 2 | 117 ÷ 77 = 1 remainder 40 |
| 3 | 77 ÷ 40 = 1 remainder 37 |
| 4 | 40 ÷ 37 = 1 remainder 3 |
| 5 | 37 ÷ 3 = 12 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 108 | 9180 |
| 77 and 94 | 7238 |
| 63 and 160 | 10080 |
| 193 and 25 | 4825 |
| 118 and 59 | 118 |