Least Common Multiple (LCM) of 20 and 105
The least common multiple (LCM) of 20 and 105 is 420.
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 105?
First, calculate the GCD of 20 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 105 = 0 remainder 20 |
| 2 | 105 ÷ 20 = 5 remainder 5 |
| 3 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 172 | 5676 |
| 121 and 94 | 11374 |
| 13 and 49 | 637 |
| 175 and 50 | 350 |
| 113 and 117 | 13221 |