Least Common Multiple (LCM) of 84 and 149
The least common multiple (LCM) of 84 and 149 is 12516.
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 84 and 149?
First, calculate the GCD of 84 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 149 = 0 remainder 84 |
| 2 | 149 ÷ 84 = 1 remainder 65 |
| 3 | 84 ÷ 65 = 1 remainder 19 |
| 4 | 65 ÷ 19 = 3 remainder 8 |
| 5 | 19 ÷ 8 = 2 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 71 | 12425 |
| 118 and 182 | 10738 |
| 138 and 92 | 276 |
| 167 and 67 | 11189 |
| 19 and 169 | 3211 |