Least Common Multiple (LCM) of 20 and 147
The least common multiple (LCM) of 20 and 147 is 2940.
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 147?
First, calculate the GCD of 20 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 147 = 0 remainder 20 |
| 2 | 147 ÷ 20 = 7 remainder 7 |
| 3 | 20 ÷ 7 = 2 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 189 | 378 |
| 126 and 122 | 7686 |
| 150 and 61 | 9150 |
| 176 and 20 | 880 |
| 66 and 58 | 1914 |