Least Common Multiple (LCM) of 63 and 125
The least common multiple (LCM) of 63 and 125 is 7875.
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 63 and 125?
First, calculate the GCD of 63 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 125 = 0 remainder 63 |
| 2 | 125 ÷ 63 = 1 remainder 62 |
| 3 | 63 ÷ 62 = 1 remainder 1 |
| 4 | 62 ÷ 1 = 62 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 177 | 2478 |
| 14 and 165 | 2310 |
| 74 and 199 | 14726 |
| 138 and 173 | 23874 |
| 120 and 190 | 2280 |