Least Common Multiple (LCM) of 53 and 164
The least common multiple (LCM) of 53 and 164 is 8692.
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 53 and 164?
First, calculate the GCD of 53 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 164 = 0 remainder 53 |
| 2 | 164 ÷ 53 = 3 remainder 5 |
| 3 | 53 ÷ 5 = 10 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 95 | 10260 |
| 40 and 16 | 80 |
| 25 and 172 | 4300 |
| 135 and 165 | 1485 |
| 162 and 75 | 4050 |