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 |
|---|---|
| 100 and 179 | 17900 |
| 103 and 98 | 10094 |
| 81 and 44 | 3564 |
| 56 and 172 | 2408 |
| 85 and 119 | 595 |