Least Common Multiple (LCM) of 30 and 51
The least common multiple (LCM) of 30 and 51 is 510.
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 30 and 51?
First, calculate the GCD of 30 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 51 = 0 remainder 30 |
| 2 | 51 ÷ 30 = 1 remainder 21 |
| 3 | 30 ÷ 21 = 1 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 13 | 2158 |
| 59 and 60 | 3540 |
| 18 and 102 | 306 |
| 80 and 94 | 3760 |
| 79 and 171 | 13509 |