Least Common Multiple (LCM) of 51 and 67
The least common multiple (LCM) of 51 and 67 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 51 and 67?
First, calculate the GCD of 51 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 67 = 0 remainder 51 |
| 2 | 67 ÷ 51 = 1 remainder 16 |
| 3 | 51 ÷ 16 = 3 remainder 3 |
| 4 | 16 ÷ 3 = 5 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 171 | 2736 |
| 178 and 133 | 23674 |
| 84 and 26 | 1092 |
| 120 and 174 | 3480 |
| 47 and 129 | 6063 |