Least Common Multiple (LCM) of 30 and 57
The least common multiple (LCM) of 30 and 57 is 570.
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 57?
First, calculate the GCD of 30 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 57 = 0 remainder 30 |
| 2 | 57 ÷ 30 = 1 remainder 27 |
| 3 | 30 ÷ 27 = 1 remainder 3 |
| 4 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 130 | 7410 |
| 52 and 135 | 7020 |
| 138 and 106 | 7314 |
| 117 and 83 | 9711 |
| 89 and 89 | 89 |