Least Common Multiple (LCM) of 125 and 144
The least common multiple (LCM) of 125 and 144 is 18000.
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 125 and 144?
First, calculate the GCD of 125 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 144 = 0 remainder 125 |
| 2 | 144 ÷ 125 = 1 remainder 19 |
| 3 | 125 ÷ 19 = 6 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 101 | 5858 |
| 56 and 77 | 616 |
| 29 and 114 | 3306 |
| 53 and 160 | 8480 |
| 163 and 92 | 14996 |