Least Common Multiple (LCM) of 101 and 125
The least common multiple (LCM) of 101 and 125 is 12625.
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 101 and 125?
First, calculate the GCD of 101 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 125 = 0 remainder 101 |
| 2 | 125 ÷ 101 = 1 remainder 24 |
| 3 | 101 ÷ 24 = 4 remainder 5 |
| 4 | 24 ÷ 5 = 4 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 139 | 139 |
| 122 and 137 | 16714 |
| 54 and 149 | 8046 |
| 200 and 194 | 19400 |
| 107 and 164 | 17548 |