Least Common Multiple (LCM) of 12 and 149
The least common multiple (LCM) of 12 and 149 is 1788.
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 12 and 149?
First, calculate the GCD of 12 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 149 = 0 remainder 12 |
| 2 | 149 ÷ 12 = 12 remainder 5 |
| 3 | 12 ÷ 5 = 2 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 172 | 12900 |
| 15 and 90 | 90 |
| 105 and 137 | 14385 |
| 103 and 78 | 8034 |
| 164 and 53 | 8692 |