Least Common Multiple (LCM) of 117 and 73
The least common multiple (LCM) of 117 and 73 is 8541.
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 73?
First, calculate the GCD of 117 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 73 = 1 remainder 44 |
| 2 | 73 ÷ 44 = 1 remainder 29 |
| 3 | 44 ÷ 29 = 1 remainder 15 |
| 4 | 29 ÷ 15 = 1 remainder 14 |
| 5 | 15 ÷ 14 = 1 remainder 1 |
| 6 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 41 | 1804 |
| 105 and 26 | 2730 |
| 47 and 125 | 5875 |
| 46 and 125 | 5750 |
| 103 and 136 | 14008 |