Least Common Multiple (LCM) of 41 and 149
The least common multiple (LCM) of 41 and 149 is 6109.
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 41 and 149?
First, calculate the GCD of 41 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 149 = 0 remainder 41 |
| 2 | 149 ÷ 41 = 3 remainder 26 |
| 3 | 41 ÷ 26 = 1 remainder 15 |
| 4 | 26 ÷ 15 = 1 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 14 | 1246 |
| 42 and 152 | 3192 |
| 74 and 144 | 5328 |
| 137 and 49 | 6713 |
| 57 and 167 | 9519 |