Least Common Multiple (LCM) of 154 and 189
The least common multiple (LCM) of 154 and 189 is 4158.
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 189?
First, calculate the GCD of 154 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 189 = 0 remainder 154 |
| 2 | 189 ÷ 154 = 1 remainder 35 |
| 3 | 154 ÷ 35 = 4 remainder 14 |
| 4 | 35 ÷ 14 = 2 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 130 | 14170 |
| 174 and 32 | 2784 |
| 182 and 182 | 182 |
| 106 and 164 | 8692 |
| 140 and 179 | 25060 |