Least Common Multiple (LCM) of 30 and 116
The least common multiple (LCM) of 30 and 116 is 1740.
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 116?
First, calculate the GCD of 30 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 116 = 0 remainder 30 |
| 2 | 116 ÷ 30 = 3 remainder 26 |
| 3 | 30 ÷ 26 = 1 remainder 4 |
| 4 | 26 ÷ 4 = 6 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 142 | 3550 |
| 129 and 139 | 17931 |
| 87 and 153 | 4437 |
| 176 and 87 | 15312 |
| 180 and 60 | 180 |