Least Common Multiple (LCM) of 20 and 101
The least common multiple (LCM) of 20 and 101 is 2020.
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 20 and 101?
First, calculate the GCD of 20 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 101 = 0 remainder 20 |
| 2 | 101 ÷ 20 = 5 remainder 1 |
| 3 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 29 | 4060 |
| 116 and 36 | 1044 |
| 53 and 82 | 4346 |
| 118 and 131 | 15458 |
| 115 and 25 | 575 |