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 |
|---|---|
| 110 and 59 | 6490 |
| 103 and 114 | 11742 |
| 174 and 64 | 5568 |
| 155 and 50 | 1550 |
| 184 and 115 | 920 |