Least Common Multiple (LCM) of 117 and 179
The least common multiple (LCM) of 117 and 179 is 20943.
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 179?
First, calculate the GCD of 117 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 179 = 0 remainder 117 |
| 2 | 179 ÷ 117 = 1 remainder 62 |
| 3 | 117 ÷ 62 = 1 remainder 55 |
| 4 | 62 ÷ 55 = 1 remainder 7 |
| 5 | 55 ÷ 7 = 7 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 89 | 10502 |
| 159 and 171 | 9063 |
| 67 and 35 | 2345 |
| 198 and 112 | 11088 |
| 193 and 175 | 33775 |