Least Common Multiple (LCM) of 114 and 154
The least common multiple (LCM) of 114 and 154 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 114 and 154?
First, calculate the GCD of 114 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 154 = 0 remainder 114 |
| 2 | 154 ÷ 114 = 1 remainder 40 |
| 3 | 114 ÷ 40 = 2 remainder 34 |
| 4 | 40 ÷ 34 = 1 remainder 6 |
| 5 | 34 ÷ 6 = 5 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 26 | 832 |
| 164 and 27 | 4428 |
| 87 and 17 | 1479 |
| 38 and 190 | 190 |
| 153 and 36 | 612 |