Least Common Multiple (LCM) of 65 and 179
The least common multiple (LCM) of 65 and 179 is 11635.
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 65 and 179?
First, calculate the GCD of 65 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 179 = 0 remainder 65 |
| 2 | 179 ÷ 65 = 2 remainder 49 |
| 3 | 65 ÷ 49 = 1 remainder 16 |
| 4 | 49 ÷ 16 = 3 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 89 | 2225 |
| 194 and 98 | 9506 |
| 58 and 187 | 10846 |
| 83 and 87 | 7221 |
| 180 and 149 | 26820 |