Least Common Multiple (LCM) of 149 and 114
The least common multiple (LCM) of 149 and 114 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 149 and 114?
First, calculate the GCD of 149 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 114 = 1 remainder 35 |
| 2 | 114 ÷ 35 = 3 remainder 9 |
| 3 | 35 ÷ 9 = 3 remainder 8 |
| 4 | 9 ÷ 8 = 1 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 75 | 13200 |
| 88 and 43 | 3784 |
| 114 and 133 | 798 |
| 141 and 40 | 5640 |
| 83 and 34 | 2822 |