Least Common Multiple (LCM) of 179 and 116
The least common multiple (LCM) of 179 and 116 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 179 and 116?
First, calculate the GCD of 179 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 116 = 1 remainder 63 |
| 2 | 116 ÷ 63 = 1 remainder 53 |
| 3 | 63 ÷ 53 = 1 remainder 10 |
| 4 | 53 ÷ 10 = 5 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 184 | 4048 |
| 88 and 178 | 7832 |
| 105 and 100 | 2100 |
| 157 and 147 | 23079 |
| 36 and 110 | 1980 |