Least Common Multiple (LCM) of 38 and 149
The least common multiple (LCM) of 38 and 149 is 5662.
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 38 and 149?
First, calculate the GCD of 38 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 149 = 0 remainder 38 |
| 2 | 149 ÷ 38 = 3 remainder 35 |
| 3 | 38 ÷ 35 = 1 remainder 3 |
| 4 | 35 ÷ 3 = 11 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 129 | 23736 |
| 117 and 17 | 1989 |
| 119 and 63 | 1071 |
| 65 and 169 | 845 |
| 135 and 155 | 4185 |