Least Common Multiple (LCM) of 117 and 20
The least common multiple (LCM) of 117 and 20 is 2340.
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 20?
First, calculate the GCD of 117 and 20 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 20 = 5 remainder 17 |
| 2 | 20 ÷ 17 = 1 remainder 3 |
| 3 | 17 ÷ 3 = 5 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 180 | 6300 |
| 153 and 68 | 612 |
| 30 and 80 | 240 |
| 66 and 180 | 1980 |
| 186 and 106 | 9858 |