Least Common Multiple (LCM) of 164 and 87
The least common multiple (LCM) of 164 and 87 is 14268.
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 87?
First, calculate the GCD of 164 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 87 = 1 remainder 77 |
| 2 | 87 ÷ 77 = 1 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 |
|---|---|
| 80 and 114 | 4560 |
| 160 and 127 | 20320 |
| 199 and 77 | 15323 |
| 190 and 31 | 5890 |
| 84 and 65 | 5460 |