Least Common Multiple (LCM) of 125 and 45
The least common multiple (LCM) of 125 and 45 is 1125.
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 45?
First, calculate the GCD of 125 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 45 = 2 remainder 35 |
| 2 | 45 ÷ 35 = 1 remainder 10 |
| 3 | 35 ÷ 10 = 3 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 15 | 2670 |
| 123 and 177 | 7257 |
| 31 and 108 | 3348 |
| 107 and 92 | 9844 |
| 185 and 119 | 22015 |