Least Common Multiple (LCM) of 65 and 184
The least common multiple (LCM) of 65 and 184 is 11960.
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 184?
First, calculate the GCD of 65 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 184 = 0 remainder 65 |
| 2 | 184 ÷ 65 = 2 remainder 54 |
| 3 | 65 ÷ 54 = 1 remainder 11 |
| 4 | 54 ÷ 11 = 4 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 160 | 480 |
| 169 and 161 | 27209 |
| 164 and 172 | 7052 |
| 168 and 139 | 23352 |
| 110 and 182 | 10010 |