Least Common Multiple (LCM) of 164 and 77
The least common multiple (LCM) of 164 and 77 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 164 and 77?
First, calculate the GCD of 164 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 77 = 2 remainder 10 |
| 2 | 77 ÷ 10 = 7 remainder 7 |
| 3 | 10 ÷ 7 = 1 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 35 | 105 |
| 113 and 98 | 11074 |
| 75 and 144 | 3600 |
| 79 and 15 | 1185 |
| 171 and 71 | 12141 |