Least Common Multiple (LCM) of 154 and 114
The least common multiple (LCM) of 154 and 114 is 8778.
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 114?
First, calculate the GCD of 154 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 114 = 1 remainder 40 |
| 2 | 114 ÷ 40 = 2 remainder 34 |
| 3 | 40 ÷ 34 = 1 remainder 6 |
| 4 | 34 ÷ 6 = 5 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 153 | 6579 |
| 198 and 123 | 8118 |
| 183 and 65 | 11895 |
| 157 and 156 | 24492 |
| 128 and 42 | 2688 |