Least Common Multiple (LCM) of 54 and 149
The least common multiple (LCM) of 54 and 149 is 8046.
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 54 and 149?
First, calculate the GCD of 54 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 149 = 0 remainder 54 |
| 2 | 149 ÷ 54 = 2 remainder 41 |
| 3 | 54 ÷ 41 = 1 remainder 13 |
| 4 | 41 ÷ 13 = 3 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 11 | 1496 |
| 37 and 176 | 6512 |
| 164 and 19 | 3116 |
| 14 and 31 | 434 |
| 11 and 102 | 1122 |