Least Common Multiple (LCM) of 116 and 179
The least common multiple (LCM) of 116 and 179 is 20764.
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 116 and 179?
First, calculate the GCD of 116 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 179 = 0 remainder 116 |
| 2 | 179 ÷ 116 = 1 remainder 63 |
| 3 | 116 ÷ 63 = 1 remainder 53 |
| 4 | 63 ÷ 53 = 1 remainder 10 |
| 5 | 53 ÷ 10 = 5 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 185 | 9435 |
| 136 and 142 | 9656 |
| 144 and 121 | 17424 |
| 100 and 50 | 100 |
| 13 and 23 | 299 |