Least Common Multiple (LCM) of 51 and 195
The least common multiple (LCM) of 51 and 195 is 3315.
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 195?
First, calculate the GCD of 51 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 195 = 0 remainder 51 |
| 2 | 195 ÷ 51 = 3 remainder 42 |
| 3 | 51 ÷ 42 = 1 remainder 9 |
| 4 | 42 ÷ 9 = 4 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 14 | 714 |
| 27 and 37 | 999 |
| 61 and 110 | 6710 |
| 190 and 155 | 5890 |
| 71 and 167 | 11857 |