Least Common Multiple (LCM) of 117 and 144
The least common multiple (LCM) of 117 and 144 is 1872.
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 117 and 144?
First, calculate the GCD of 117 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 144 = 0 remainder 117 |
| 2 | 144 ÷ 117 = 1 remainder 27 |
| 3 | 117 ÷ 27 = 4 remainder 9 |
| 4 | 27 ÷ 9 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 58 | 3190 |
| 130 and 11 | 1430 |
| 59 and 178 | 10502 |
| 142 and 189 | 26838 |
| 113 and 108 | 12204 |