Least Common Multiple (LCM) of 164 and 117
The least common multiple (LCM) of 164 and 117 is 19188.
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 117?
First, calculate the GCD of 164 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 117 = 1 remainder 47 |
| 2 | 117 ÷ 47 = 2 remainder 23 |
| 3 | 47 ÷ 23 = 2 remainder 1 |
| 4 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 31 | 372 |
| 200 and 135 | 5400 |
| 71 and 128 | 9088 |
| 170 and 70 | 1190 |
| 165 and 186 | 10230 |