Least Common Multiple (LCM) of 179 and 117
The least common multiple (LCM) of 179 and 117 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 179 and 117?
First, calculate the GCD of 179 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 117 = 1 remainder 62 |
| 2 | 117 ÷ 62 = 1 remainder 55 |
| 3 | 62 ÷ 55 = 1 remainder 7 |
| 4 | 55 ÷ 7 = 7 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 20 | 300 |
| 79 and 161 | 12719 |
| 87 and 143 | 12441 |
| 163 and 142 | 23146 |
| 87 and 30 | 870 |