Least Common Multiple (LCM) of 59 and 144
The least common multiple (LCM) of 59 and 144 is 8496.
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 59 and 144?
First, calculate the GCD of 59 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 144 = 0 remainder 59 |
| 2 | 144 ÷ 59 = 2 remainder 26 |
| 3 | 59 ÷ 26 = 2 remainder 7 |
| 4 | 26 ÷ 7 = 3 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 72 | 6840 |
| 33 and 105 | 1155 |
| 62 and 71 | 4402 |
| 116 and 58 | 116 |
| 12 and 132 | 132 |