Least Common Multiple (LCM) of 20 and 154
The least common multiple (LCM) of 20 and 154 is 1540.
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 154?
First, calculate the GCD of 20 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 154 = 0 remainder 20 |
| 2 | 154 ÷ 20 = 7 remainder 14 |
| 3 | 20 ÷ 14 = 1 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 102 | 11526 |
| 118 and 39 | 4602 |
| 127 and 88 | 11176 |
| 178 and 185 | 32930 |
| 102 and 58 | 2958 |