Least Common Multiple (LCM) of 125 and 107
The least common multiple (LCM) of 125 and 107 is 13375.
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 107?
First, calculate the GCD of 125 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 107 = 1 remainder 18 |
| 2 | 107 ÷ 18 = 5 remainder 17 |
| 3 | 18 ÷ 17 = 1 remainder 1 |
| 4 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 135 | 135 |
| 138 and 73 | 10074 |
| 98 and 45 | 4410 |
| 161 and 45 | 7245 |
| 104 and 93 | 9672 |