Least Common Multiple (LCM) of 154 and 180
The least common multiple (LCM) of 154 and 180 is 13860.
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 154 and 180?
First, calculate the GCD of 154 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 180 = 0 remainder 154 |
| 2 | 180 ÷ 154 = 1 remainder 26 |
| 3 | 154 ÷ 26 = 5 remainder 24 |
| 4 | 26 ÷ 24 = 1 remainder 2 |
| 5 | 24 ÷ 2 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 165 | 7755 |
| 158 and 32 | 2528 |
| 117 and 156 | 468 |
| 167 and 184 | 30728 |
| 18 and 90 | 90 |