Least Common Multiple (LCM) of 109 and 144
The least common multiple (LCM) of 109 and 144 is 15696.
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 109 and 144?
First, calculate the GCD of 109 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 144 = 0 remainder 109 |
| 2 | 144 ÷ 109 = 1 remainder 35 |
| 3 | 109 ÷ 35 = 3 remainder 4 |
| 4 | 35 ÷ 4 = 8 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 125 | 21125 |
| 43 and 172 | 172 |
| 39 and 90 | 1170 |
| 41 and 122 | 5002 |
| 119 and 67 | 7973 |