Least Common Multiple (LCM) of 30 and 113
The least common multiple (LCM) of 30 and 113 is 3390.
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 113?
First, calculate the GCD of 30 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 113 = 0 remainder 30 |
| 2 | 113 ÷ 30 = 3 remainder 23 |
| 3 | 30 ÷ 23 = 1 remainder 7 |
| 4 | 23 ÷ 7 = 3 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 31 | 527 |
| 182 and 182 | 182 |
| 96 and 96 | 96 |
| 53 and 68 | 3604 |
| 111 and 137 | 15207 |