Least Common Multiple (LCM) of 125 and 99
The least common multiple (LCM) of 125 and 99 is 12375.
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 99?
First, calculate the GCD of 125 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 99 = 1 remainder 26 |
| 2 | 99 ÷ 26 = 3 remainder 21 |
| 3 | 26 ÷ 21 = 1 remainder 5 |
| 4 | 21 ÷ 5 = 4 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 16 | 560 |
| 118 and 97 | 11446 |
| 162 and 152 | 12312 |
| 49 and 40 | 1960 |
| 180 and 178 | 16020 |