Least Common Multiple (LCM) of 73 and 117
The least common multiple (LCM) of 73 and 117 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 73 and 117?
First, calculate the GCD of 73 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 117 = 0 remainder 73 |
| 2 | 117 ÷ 73 = 1 remainder 44 |
| 3 | 73 ÷ 44 = 1 remainder 29 |
| 4 | 44 ÷ 29 = 1 remainder 15 |
| 5 | 29 ÷ 15 = 1 remainder 14 |
| 6 | 15 ÷ 14 = 1 remainder 1 |
| 7 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 25 | 725 |
| 189 and 105 | 945 |
| 200 and 120 | 600 |
| 172 and 191 | 32852 |
| 123 and 122 | 15006 |