Least Common Multiple (LCM) of 117 and 23
The least common multiple (LCM) of 117 and 23 is 2691.
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 23?
First, calculate the GCD of 117 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 23 = 5 remainder 2 |
| 2 | 23 ÷ 2 = 11 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 144 | 1008 |
| 79 and 46 | 3634 |
| 102 and 128 | 6528 |
| 96 and 55 | 5280 |
| 147 and 174 | 8526 |