Least Common Multiple (LCM) of 114 and 149
The least common multiple (LCM) of 114 and 149 is 16986.
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 149?
First, calculate the GCD of 114 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 149 = 0 remainder 114 |
| 2 | 149 ÷ 114 = 1 remainder 35 |
| 3 | 114 ÷ 35 = 3 remainder 9 |
| 4 | 35 ÷ 9 = 3 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 31 | 3565 |
| 118 and 178 | 10502 |
| 141 and 80 | 11280 |
| 39 and 67 | 2613 |
| 22 and 23 | 506 |