Least Common Multiple (LCM) of 51 and 58
The least common multiple (LCM) of 51 and 58 is 2958.
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 58?
First, calculate the GCD of 51 and 58 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 58 = 0 remainder 51 |
| 2 | 58 ÷ 51 = 1 remainder 7 |
| 3 | 51 ÷ 7 = 7 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 128 | 17536 |
| 145 and 89 | 12905 |
| 31 and 190 | 5890 |
| 85 and 75 | 1275 |
| 180 and 29 | 5220 |