Least Common Multiple (LCM) of 101 and 30
The least common multiple (LCM) of 101 and 30 is 3030.
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 101 and 30?
First, calculate the GCD of 101 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 30 = 3 remainder 11 |
| 2 | 30 ÷ 11 = 2 remainder 8 |
| 3 | 11 ÷ 8 = 1 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 144 | 9648 |
| 54 and 120 | 1080 |
| 195 and 23 | 4485 |
| 171 and 194 | 33174 |
| 142 and 60 | 4260 |