Least Common Multiple (LCM) of 114 and 164
The least common multiple (LCM) of 114 and 164 is 9348.
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 114 and 164?
First, calculate the GCD of 114 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 164 = 0 remainder 114 |
| 2 | 164 ÷ 114 = 1 remainder 50 |
| 3 | 114 ÷ 50 = 2 remainder 14 |
| 4 | 50 ÷ 14 = 3 remainder 8 |
| 5 | 14 ÷ 8 = 1 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 171 | 16587 |
| 193 and 24 | 4632 |
| 89 and 88 | 7832 |
| 159 and 126 | 6678 |
| 175 and 200 | 1400 |