Least Common Multiple (LCM) of 145 and 114
The least common multiple (LCM) of 145 and 114 is 16530.
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 145 and 114?
First, calculate the GCD of 145 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 114 = 1 remainder 31 |
| 2 | 114 ÷ 31 = 3 remainder 21 |
| 3 | 31 ÷ 21 = 1 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 106 | 9434 |
| 138 and 14 | 966 |
| 99 and 89 | 8811 |
| 117 and 33 | 1287 |
| 170 and 127 | 21590 |