Least Common Multiple (LCM) of 117 and 164
The least common multiple (LCM) of 117 and 164 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 117 and 164?
First, calculate the GCD of 117 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 164 = 0 remainder 117 |
| 2 | 164 ÷ 117 = 1 remainder 47 |
| 3 | 117 ÷ 47 = 2 remainder 23 |
| 4 | 47 ÷ 23 = 2 remainder 1 |
| 5 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 13 | 949 |
| 108 and 21 | 756 |
| 141 and 130 | 18330 |
| 57 and 112 | 6384 |
| 32 and 198 | 3168 |