Least Common Multiple (LCM) of 30 and 133
The least common multiple (LCM) of 30 and 133 is 3990.
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 133?
First, calculate the GCD of 30 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 133 = 0 remainder 30 |
| 2 | 133 ÷ 30 = 4 remainder 13 |
| 3 | 30 ÷ 13 = 2 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 155 | 16895 |
| 172 and 63 | 10836 |
| 141 and 120 | 5640 |
| 63 and 11 | 693 |
| 140 and 126 | 1260 |