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 |
|---|---|
| 114 and 67 | 7638 |
| 150 and 192 | 4800 |
| 163 and 169 | 27547 |
| 131 and 69 | 9039 |
| 61 and 23 | 1403 |