Least Common Multiple (LCM) of 51 and 189
The least common multiple (LCM) of 51 and 189 is 3213.
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 189?
First, calculate the GCD of 51 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 189 = 0 remainder 51 |
| 2 | 189 ÷ 51 = 3 remainder 36 |
| 3 | 51 ÷ 36 = 1 remainder 15 |
| 4 | 36 ÷ 15 = 2 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 20 | 580 |
| 144 and 46 | 3312 |
| 182 and 150 | 13650 |
| 66 and 32 | 1056 |
| 100 and 115 | 2300 |