Least Common Multiple (LCM) of 77 and 164
The least common multiple (LCM) of 77 and 164 is 12628.
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 164?
First, calculate the GCD of 77 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 164 = 0 remainder 77 |
| 2 | 164 ÷ 77 = 2 remainder 10 |
| 3 | 77 ÷ 10 = 7 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 188 | 6768 |
| 161 and 85 | 13685 |
| 119 and 158 | 18802 |
| 168 and 33 | 1848 |
| 45 and 121 | 5445 |