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 |
|---|---|
| 41 and 188 | 7708 |
| 17 and 31 | 527 |
| 121 and 122 | 14762 |
| 157 and 87 | 13659 |
| 100 and 24 | 600 |