Least Common Multiple (LCM) of 30 and 114
The least common multiple (LCM) of 30 and 114 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 114?
First, calculate the GCD of 30 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 114 = 0 remainder 30 |
| 2 | 114 ÷ 30 = 3 remainder 24 |
| 3 | 30 ÷ 24 = 1 remainder 6 |
| 4 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 117 | 4095 |
| 195 and 191 | 37245 |
| 93 and 119 | 11067 |
| 195 and 76 | 14820 |
| 86 and 40 | 1720 |