Least Common Multiple (LCM) of 51 and 184
The least common multiple (LCM) of 51 and 184 is 9384.
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 51 and 184?
First, calculate the GCD of 51 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 184 = 0 remainder 51 |
| 2 | 184 ÷ 51 = 3 remainder 31 |
| 3 | 51 ÷ 31 = 1 remainder 20 |
| 4 | 31 ÷ 20 = 1 remainder 11 |
| 5 | 20 ÷ 11 = 1 remainder 9 |
| 6 | 11 ÷ 9 = 1 remainder 2 |
| 7 | 9 ÷ 2 = 4 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 190 | 4370 |
| 70 and 18 | 630 |
| 136 and 136 | 136 |
| 136 and 116 | 3944 |
| 114 and 110 | 6270 |