Least Common Multiple (LCM) of 108 and 149
The least common multiple (LCM) of 108 and 149 is 16092.
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 108 and 149?
First, calculate the GCD of 108 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 149 = 0 remainder 108 |
| 2 | 149 ÷ 108 = 1 remainder 41 |
| 3 | 108 ÷ 41 = 2 remainder 26 |
| 4 | 41 ÷ 26 = 1 remainder 15 |
| 5 | 26 ÷ 15 = 1 remainder 11 |
| 6 | 15 ÷ 11 = 1 remainder 4 |
| 7 | 11 ÷ 4 = 2 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 196 | 980 |
| 88 and 157 | 13816 |
| 126 and 185 | 23310 |
| 119 and 158 | 18802 |
| 181 and 12 | 2172 |