Least Common Multiple (LCM) of 53 and 125
The least common multiple (LCM) of 53 and 125 is 6625.
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 53 and 125?
First, calculate the GCD of 53 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 125 = 0 remainder 53 |
| 2 | 125 ÷ 53 = 2 remainder 19 |
| 3 | 53 ÷ 19 = 2 remainder 15 |
| 4 | 19 ÷ 15 = 1 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 97 | 9700 |
| 143 and 36 | 5148 |
| 82 and 65 | 5330 |
| 199 and 12 | 2388 |
| 187 and 125 | 23375 |