Least Common Multiple (LCM) of 67 and 51
The least common multiple (LCM) of 67 and 51 is 3417.
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 67 and 51?
First, calculate the GCD of 67 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 51 = 1 remainder 16 |
| 2 | 51 ÷ 16 = 3 remainder 3 |
| 3 | 16 ÷ 3 = 5 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 45 | 4365 |
| 120 and 48 | 240 |
| 36 and 14 | 252 |
| 86 and 49 | 4214 |
| 180 and 11 | 1980 |