Least Common Multiple (LCM) of 77 and 118
The least common multiple (LCM) of 77 and 118 is 9086.
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 118?
First, calculate the GCD of 77 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 118 = 0 remainder 77 |
| 2 | 118 ÷ 77 = 1 remainder 41 |
| 3 | 77 ÷ 41 = 1 remainder 36 |
| 4 | 41 ÷ 36 = 1 remainder 5 |
| 5 | 36 ÷ 5 = 7 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 173 | 21279 |
| 123 and 106 | 13038 |
| 45 and 64 | 2880 |
| 141 and 162 | 7614 |
| 142 and 184 | 13064 |