Least Common Multiple (LCM) of 144 and 149
The least common multiple (LCM) of 144 and 149 is 21456.
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 144 and 149?
First, calculate the GCD of 144 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 149 = 0 remainder 144 |
| 2 | 149 ÷ 144 = 1 remainder 5 |
| 3 | 144 ÷ 5 = 28 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 35 | 6020 |
| 39 and 182 | 546 |
| 34 and 186 | 3162 |
| 129 and 23 | 2967 |
| 23 and 39 | 897 |